# NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area - Download PDF

**NCERT Solutions for Perimeter and area class 7 -** If you want to cover the floor of the room. The first question that comes in mind is how many square meters of flooring you need? It can be done by measuring the area of the room. In the practical case, you will buy slightly higher than the required area since there may be cuts and joints required for the flooring. The perimeter can be calculated by adding the length of all sides of the closed figure. In this chapter, you will study the perimeters of some simple geometry like rectangle, triangle, parallelogram, and circles.

You should try to solve all the NCERT problems including examples for a better understanding of the concepts. In CBSE NCERT solution for Class 7 Maths chapter 11 Perimeter and Area, you will get some complex geometry problems which will give you more clarity. You can get NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get solutions to four exercises of this chapter. Students are supposed to refer to the NCERT Class 7 Syllabus and know the exam pattern and important topics.

## NCERT Solutions for Maths Chapter 11 Perimeter and Area Class 7 - Important Formulae

Perimeter of a Triangle = Side_{1} + Side_{2} + Side_{3}

Perimeter of a Square = 4 × side of square

Perimeter of a Rectangle = 2 × ( Length + Breadth or Width )

Circumference or Perimeter of a Circle = πd = 2πr

Where d = Diameter of circle = 2r, r = Radius of circle

Area of a Square = Side × Side

Area of rectangle = Length × Breadth

Congruent parts of rectangle:

The area of each congruent part = (1/2) × ( The area of the rectangle )

Area of a parallelogram = Base × Height

Area of a Triangle = (1/2) × ( Base) × ( Height)

All the congruent triangles are equal in the area but the triangles equal in the area need not be congruent.

Area of a circle = πr2 where, r = Radius of circle

Unit Conversions:

1 cm^{2} = 100 mm^{2}

1 m^{2} = 10000 cm^{2}

1 hectare = 10000 m2

## NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area - Important Points

**Perimeter:** The total length of the boundary of a two-dimensional shape.

**Circumference:** The distance around the boundary of a circle.

**Area:** The measure of the space enclosed by a two-dimensional shape.

**Congruent:** Two shapes are congruent if they have the same size and shape.

**Base:** The bottom side of a two-dimensional shape, like a parallelogram or triangle.

**Height:** The perpendicular distance between the base and the opposite side in a two-dimensional shape.

**Diameter:** The longest chord (line segment connecting two points on a circle) passing through the center of a circle.

**Radius:** The distance from the center of a circle to any point on its boundary.

**Unit Conversions:** Converting measurements from one unit to another, based on their relationships.

Free download **NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area PDF **for CBSE Exam.

## NCERT Solutions for Maths Chapter 11 Perimeter and Area Class 7

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## NCERT Solution for Class 7 Maths Chapter 11 Perimeter and Area (Intext Questions and Exercise)

**NCERT Solutions for Maths Chapter 11 Perimeter and Area Class 7 Topic 11.2 **

**Question:1 **What would you need to find, area or perimeter, to answer the following?

How much space does a blackboard occupy?

**Answer: **The space of the board includes the whole area of the board

** Question:2 **What would you need to find, area or perimeter, to answer the following?

What is the length of a wire required to fence a rectangular flower bed?

** Answer**: The length of the wire to fence a flower bed is the circumference of the flower bed

** Question:3 **What would you need to find, area or perimeter, to answer the following?

What distance would you cover by taking two rounds of a triangular park?

** Answer: **Distance covered by taking round a triangular park is equal to the ** circumference ** of the triangular park

** Question:4 **What would you need to find, area or perimeter, to answer the following?

How much plastic sheet do you need to cover a rectangular swimming pool?

** Answer: **Plastic sheet need to cover is the **area **of the rectangular swimming pool

** Question:2 **Give two examples where the area increases as the perimeter increases.

** Answer**: A square of side 1m has perimeter 4 m and area 1 m ^{ 2 } . When all sides are increased by 1m then perimeter =8m and area= 4 m ^{ 2 } . Similarly, if we increase the length from 6m to 9m and breadth from 3m to 6m of a rectangular the perimeter and area will increase

** Question:3 **Give two examples where the area does not increase when perimeter increases.

** Answer: **Area of a rectangle with length = 20cm, breadth = 5 cm is 100cm ^{ 2 } and perimeter is 50 cm. A rectangle with sides 50 cm and 2 cm ha area = 100cm ^{ 2 } but perimeter is 104 cm

**NCERT Solutions for Maths Chapter 11 Perimeter and Area Class 7 Exercise: 11.1 **

**Question: ****1(i) ** The length and the breadth of a rectangular piece of land are and respectively. Find its area

**Answer: **It is given that the length and the breadth of a rectangular piece of land are and

Now, we know that

Area of the rectangle (A) =

Therefore, area of rectangular piece of land is

** Question: ****1(ii) ** The length and the breadth of a rectangular piece of land are and respectively. Find the cost of the land, if of the land costs

** Answer: **It is given that the length and the breadth of a rectangular piece of land are and

Now, we know that

Area of the rectangle (A) =

Now, it is given that of the land costs

Therefore, cost of of land is

** Question: ****2 ** Find the area of a square park whose perimeter is .

** Answer: **It is given that the perimeter of the square park is

Now, we know that

The perimeter of a square is (P) , where a is the side of the square

Now,

Area of the square (A)

Therefore, the area of a square park is

** Question: ****3 ** Find the breadth of a rectangular plot of land, if its area is and the length is . Also find its perimeter.

** Answer: **It is given that the area of rectangular land is and the length is

Now, we know that

Area of rectangle is

Now,

The perimeter of the rectangle is

Therefore, the breath and perimeter of the rectangle are 20m and 88m respectively

** Question: ****4 ** The perimeter of a rectangular sheet is . If the length is , find its breadth. Also find the area.

** Answer: **It is given that perimeter of a rectangular sheet is and length is

Now, we know that

The perimeter of the rectangle is

Now,

Area of rectangle is

Therefore, breath and area of the rectangle are 15cm and respectively

**Question: ****5 ** The area of a square park is the same as of a rectangular park. If the side of the square park is and the length of the rectangular park is , find the breadth of the rectangular park

** Answer: **It is given that the area of a square park is the same as of a rectangular park and side of the square park is and the length of the rectangular park is

Now, we know that

Area of square

Area of rectangle

Area of square = Area of rectangle

Therefore, breadth of the rectangle is 40 m

** Question: ****6 ** A wire is in the shape of a rectangle. Its length is and breadth is . If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

** Answer: **It is given that the length of rectangular wire is and breadth is .

Now, if it reshaped into a square wire

Then,

The perimeter of rectangle = perimeter of the square

Now,

Area of rectangle

Area of square

Therefore, the side of the square is 31 cm and we can clearly see that square-shaped wire encloses more area

** Question: ****7 ** The perimeter of a rectangle is . If the breadth of the rectangle is , find its length. Also find the area of the rectangle.

** Answer: **It is given that the perimeter of a rectangle is and breadth is

Now, we know that

The perimeter of the rectangle is

Now,

Area of rectangle is

Therefore, the length and area of the rectangle are 35cm and respectively

**Question: ****8 ** A door of length and breadth is fitted in a wall. The length of the wall is and the breadth is (Fig11.6). Find the cost of white washing the wall, if the rate of white washing the wall is

** Answer: **It is given that the length of door is and breadth is and the length of the wall is and the breadth is

Now, we know that

Area of rectangle is

Thus, the area of the wall is

And

Area of the door is

Now, Area to be painted = Area of wall - Area of door = 16.2 - 2 = 14.2

Now, the cost of whitewashing the wall, at the rate of is

Therefore, the cost of whitewashing the wall, at the rate of is Rs 284

** NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Topic 11.2.2**** **

**Question ****1: ** Each of the following rectangles of length 6 cm and breadth 4 cm is composed of congruent polygons. Find the area of each polygon.

** Answer: **

The total area of rectangle

i) The first rectangle is divided into 6 equal parts. So the area of each part will be one-sixth of the total area

ii) The rectangle is divided into 4 equal parts, area of each part= one-forth area of rectangle= 6 cm ^{ 2 }

iii) and (iv) are divided into two equal parts. Area of each part will be one half the total area of rectangle= 12 cm ^{ 2 }

v) Area of rectangle is divided into 8 equal parts. Area of one part is one-eighth of the total area of rectangle = 3 cm ^{ 2 }

**NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Topic 11.3 **

** Question:1(i) **Find the area of following parallelograms:

** Answer: **Area of the parallelogram is the product of base and height

** Question: ****1(ii) ** Find the area of following parallelograms:

** Answer: **Area of the parallelogram is the product of base and height

** Question:(iii) ** Find the area of the following parallelograms:

In a parallelogram , and the perpendicular from on is

** Answer:** Area of parallelogram = the product of base and height

** NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Exercise 11.2 **

** Question: ****1(a) ** Find the area of the following parallelograms:

** Answer: **We know that

Area of parallelogram

Here,

Base of parallelogram = 7cm

and

Height of parallelogram = 4 cm

Therefore, the area of the parallelogram is

** Question: ****1(b) ** Find the area of the following parallelograms:

** Answer: **

We know that

Area of parallelogram

Here,

Base of parallelogram = 5cm

and

Height of parallelogram = 3 cm

Therefore, the area of the parallelogram is

** Question: ** ** 1(c) ** Find the area of the following parallelograms:

** Answer: **We know that

Area of parallelogram

Here,

Base of parallelogram = 2.5cm

and

Height of parallelogram = 3.5 cm

Therefore, area of parallelogram is

** Question: ****1(d) ** Find the area of the following parallelograms:

** Answer: **We know that

Area of parallelogram

Here,

Base of parallelogram = 5cm

and

Height of parallelogram = 4.8 cm

Therefore, the area of a parallelogram is

** Question: ****1(e) ** Find the area of the following parallelograms:

** Answer: **We know that

Area of parallelogram

Here,

Base of parallelogram = 2 cm

and

Height of parallelogram = 4.4 cm

Therefore, the area of a parallelogram is

** Question: ****2(a) ** Find the area of each of the following triangles:

** Answer: **We know that

Area of triangle

Here,

Base of triangle = 4 cm

and

Height of triangle =3 cm

Therefore, area of triangle is

** Question: ** ** 2(b) ** Find the area of the following triangles:

** Answer: **We know that

Area of triangle

Here,

Base of triangle = 5 cm

and

Height of triangle =3.2 cm

Therefore, the area of the triangle is

** Question: ****2(c) ** Find the area of the following triangles:

** Answer: **We know that

Area of triangle

Here,

Base of triangle = 3 cm

and

Height of triangle =4 cm

Therefore, area of triangle is

** Question: ** ** 2(d) ** Find the area of the following triangles:

** Answer: **We know that

Area of triangle

Here,

Base of triangle = 3 cm

and

Height of triangle =2 cm

Therefore, the area of the triangle is

** Question: ** ** 3 ** Find the missing values:

** Answer: **We know that

Area of parallelogram

a) Here, base and area of parallelogram is given

b) Here height and area of parallelogram is given

c) Here height and area of parallelogram is given

d) Here base and area of parallelogram is given

** Question:**** 4 ** Find the missing values:

** Answer:** We know that

Area of triangle

a) Here, the base and area of the triangle is given

b) Here height and area of the triangle is given

c) Here base and area of the triangle is given

** Question: ****5(a) ** is a parallelogram (Fig 11.23). is the height from to and is the height from to . If and

Find:

the area of the parallelogram

** Answer:** We know that

Area of parallelogram

Here,

Base of parallelogram = 12 cm

and

Height of parallelogram = 7.6 cm

Therefore, area of parallelogram is

** Question: ** ** 5(b) ** is a parallelogram (Fig 11.23). is the height from to and is the height from to . If and

Find:

, if .

** Answer: **We know that

Area of parallelogram

Here,

Base of parallelogram = 12 cm

and

Height of parallelogram = 7.6 cm

Now,

The area is also given by

Therefore, value of QN is

**Question: ****6 ** and are the heights on sides and respectively, of parallelogram (Fig 11.24). If the area of the parallelogram is and find the length of and

** Answer: **We know that

Area of parallelogram

Here,

Base of parallelogram(AB) = 35 cm

and

Height of parallelogram(DL) = h cm

Similarly,

Area is also given by

Therefore, the value of BM and DL are is 30cm and 42cm respectively

**Question:7 ** is right angled at (Fig 11.25). is perpendicular to . If and Find the area of

. Also find the length of .

** Answer:** We know that

Area of triangle

Now,

When base = 5 cm and height = 12 cm

Then, the area is equal to

Now,

When base = 13 cm and height = AD area remain same

Therefore,

Therefore, the value of AD is and the area is equal to

**Question: ****8 ** is isosceles with and (Fig 11.26). The height from to is Find the area of

What will be the height from to i.e., ?

** Answer: **We know that

Area of triangle

Now,

When base(BC) = 9 cm and height(AD) = 6 cm

Then, the area is equal to

Now,

When base(AB) = 7.5 cm and height(CE) = h , area remain same

Therefore,

Therefore, value of CE is 7.2cm and area is equal to

**NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Topic 11.5.1 **

** Question:(a) ** In Fig Which square has a larger perimeter?

** Answer: **The outer square has a larger perimeter. Since each side of the inner square forms a triangle. The length of the third side of a triangle is less than the sum of the other two lengths.

** Question:(b) ** In Fig 11.31, Which is larger, perimeter of smaller square or the circumference of the circle?

** Answer: **The arc length of the circle is slightly greater than the side length of the inner square. Therefore circumference of the inner circle is greater than the inner square

** NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Exercise 11.3 **

** Question: ****1(a) ** Find the circumference of the circles with the following radius: (Take )

** Answer:** We know that

Circumference of a circle is

Therefore, the circumference of the circle is 88 cm

** Question: ** ** 1(b) ** Find the circumference of the circles with the following radius: (Take )

** Answer: **We know that

Circumference of circle is

Therefore, the circumference of the circle is 176 mm

** Question: ** ** 1(c) ** Find the circumference of the circles with the following radius: (Take )

** Answer: **We know that

Circumference of circle is

Therefore, circumference of circle is 132 cm

** Question: ** ** 2(a) ** Find the area of the following circles, given that:

(Take )

** Answer: **We know that

Area of circle is

Therefore, the area of the circle is

** Question: ** ** 2(b) ** Find the area of the following circles, given that:

** Answer:** We know that

Area of circle is

Therefore, area of circle is

** Question: ** ** 2(c) ** Find the area of the following circles, given that:

** Answer:** We know that

Area of circle is

Therefore, the area of the circle is

** Question: ****3 ** If the circumference of a circular sheet is find its radius. Also, find the area of the sheet. (Take )

** Answer: **It is given that circumference of a circular sheet is 154 m

We know that

Circumference of circle is

Now,

Area of circle

Therefore, the radius and area of the circle are 24.5 m and respectively

** Question: ****4 ** A gardener wants to fence a circular garden of diameter . Find the length of the rope he needs to purchase if he makes rounds of fence. Also find the cost of the rope, if it costs (Take ).

** Answer:** It is given that diameter of a circular garden is .

We know that

Circumference of circle is

Now, length of the rope requires to makes rounds of fence is

circumference of circle

Now, cost of rope at is

Therefore, length of the rope requires to makes rounds of fence is 132 m and cost of rope at is Rs 528

** Question: ** ** 5 ** From a circular sheet of radius , a circle of radius is removed. Find the area of the remaining sheet.(Take )

** Answer: **We know that

Area of circle

Area of circular sheet with radius 4 cm

Area of the circular sheet with radius 3 cm

Now,

Area of remaining sheet = Area of circle with radius 4 cm - Area od circle with radius 3 cm

Therefore, Area of remaining sheet is

** Question: ****6 ** Saima wants to put a lace on the edge of a circular table cover of diameter . Find the length of the lace required and also find its cost if one meter of the lace costs (Take )

** Answer:** It is given that the diameter of a circular table is 1.5m.

We know that

Circumference of circle is

Now, length of the lace required is

circumference of circle

Now, cost of lace at is

Therefore, length of the lace required is 4.71 m and cost of lace at is Rs 70.65

** Question: ****7 ** Find the perimeter of the adjoining figure, which is a semicircle including its diameter.

** Answer: ** It is given that the diameter of semi-circle is 10 cm.

We know that

Circumference of semi circle is

Circumference of semi-circle with diameter 10 cm including diameter is

Therefore, Circumference of semi-circle with diameter 10 cm including diameter is 25.7 cm

** Question: ** ** 8 ** Find the cost of polishing a circular table-top of diameter , if the rate of polishing is . (Take )

** Answer:** It is given that the diameter of a circular table is 1.6m.

We know that

Area of circle is

Now, the cost of polishing at is

Therefore, the cost of polishing at is Rs 30.144

** Question:**** 9 ** Shazli took a wire of length and bent it into the shape of a circle. Find the radius of that circle. Also, find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take )

** Answer:** It is given that the length of wire is 44 cm

Now, we know that

Circumference of the circle (C) =

Now,

Area of circle (A) =

- (i)

Now,

Perimeter of square(P) =

Area of sqaure =

-(ii)

From equation (i) and (ii) we can clearly see that area of the circular-shaped wire is more than square-shaped wire

** Question: ****10. ** From a circular card sheet of radius , two circles of radius and a rectangle of length and breadth are removed.(as shown in the adjoining figure). Find the area of the remaining sheet. (Take )

** Answer: **It is given that radius of circular card sheet is

Now, we know that

Area of circle (A) =

- (i)

Now,

Area of circle with radius 3.5 cm is

Area of two such circle is = -(ii)

Now, Area of rectangle =

-(iii)

Now, the remaining area is (i) - [(ii) + (iii)]

Therefore, area of the remaining sheet is

** Question:****11 ** A circle of radius is cut out from a square piece of an aluminium sheet of side . What is the area of the left over aluminium sheet?

(Take )

** Answer: **It is given that the radius of the circle is

Now, we know that

Area of the circle (A) =

- (i)

Now,

Now, Area of square =

-(ii)

Now, the remaining area is (ii) - (i)

Therefore, the area of the remaining aluminium sheet is

** Question: ****12 ** The circumference of a circle is . Find the radius and the area of the circle? (Take )

** Answer: **It is given that circumference of circle is

Now, we know that

Circumference of circle is =

Now, Area of circle (A) =

Therefore, radius and area of the circle are respectively

** Question: ** ** 13 ** A circular flower bed is surrounded by a path wide. The diameter of the flower bed is . What is the area of this path?

** Answer: **It is given that the diameter of the flower bed is

Therefore,

Now, we know that

Area of the circle (A) =

-(i)

Now, Area of outer circle with radius(r ') = 33 + 4 = 37 cm is

-(ii)

Area of the path is equation (ii) - (i)

Therefore, the area of the path is

**Question:****14 ** A circular flower garden has an area of . A sprinkler at the centre of the garden can cover an area that has a radius of . Will the sprinkler water the entire garden? (Take )

** Answer: **It is given that the radius of the sprinkler is

Now, we know that

Area of the circle (A) =

Area cover by sprinkle is

And the area of the flower garden is

Therefore, ** YES ** sprinkler water the entire garden

** Question:****15 ** Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take )

** Answer: **We know that

Circumference of circle =

Now, the circumference of the inner circle with radius (r) = is

And the circumference of the outer circle with radius (r ') = 19 m is

Therefore, the circumference of inner and outer circles are respectively

** Question:****16 ** How many times a wheel of radius must rotate to go ? (Take )

** Answer: **It is given that radius of wheel is

Now, we know that

Circumference of circle =

Now, number of rotation done by wheel to go ** 352 m ** is

Therefore, number of rotation done by wheel to go 352 m is ** 200 **

** Question: ****17 ** The minute hand of a circular clock is long. How far does the tip of the minute hand move in hour. (Take )

** Answer:** It is given that minute hand of a circular clock is long i.e. ( r = 15 cm)

Now, we know that one hour means a complete circle of minute hand

Now,

Circumference of circle =

Therefore, distance cover by minute hand in one hour is ** 94.2 cm **

**NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Topic 11.6 **

**Question:(i) **Convert the following:

** Answer: **1 cm = 10 mm

therefor

** Question:(ii) **Convert the following:

** Answer:** ha represents hectare

1 ha is 10000 m ^{ 2 }

therefor

** Question:(iii) ** Convert the following:

** Answer: **1m = 100cm

Therefor

** Question:(iv) ** Convert the following:

** Answer: **The conversion is done as follows

** NCERT Solutions for Class 7th Maths Chapter 11 Perimeter and Area Exercise 11.4 **

** Question: ****1 ** A garden is long and broad. A path wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

** Answer:** It is given that the garden is long and broad

It is clear that it is rectangular shaped with

We know that the area of the rectangle is

-(i)

Now, length and breadth of the outer rectangle is

Area of the outer rectangle is

-(ii)

Area of the path is (ii) - (i)

Therefore, the area of the path is

** Question: ****2 ** A wide path runs outside and around a rectangular park of length and breadth . Find the area of the path.

** Answer: **It is given that park is long and broad

It is clear that it is rectangular shaped with

We know that area of rectangle is

-(i)

Now, length and breadth of outer rectangle is

Area of the outer rectangle is

-(ii)

Area of path is (ii) - (i)

Therefore, area of path is

**Question: ****3 ** A picture is painted on a cardboard long and wide such that there is a margin of along each of its sides. Find the total area of the margin

** Answer:** It is given that cardboard is long and wide such that there is a margin of along each of its sides

It is clear that it is rectangular shaped with

We know that the area of the rectangle is

-(i)

Now, the length and breadth of cardboard without margin is

Area of cardboard without margin is

-(ii)

Area of margin is (i) - (ii)

Therefore, the area of margin is

**Question:**** 4(i) ** A verandah of width is constructed all along outside a room which is long and wide. Find: the area of the verandah

** Answer: ** It is given that room is long and wide.

It is clear that it is rectangular shaped with

We know that the area of the rectangle is

-(i)

Now, when verandah of width is constructed all along outside the room then length and breadth of the room is

Area of the room after verandah of width is constructed

-(ii)

Area of verandah is (ii) - (i)

Therefore, the area of the verandah is

** Question: **** 4(ii) ** A verandah of width is constructed all along outside a room which is long and wide. Find: the cost of cementing the floor of the verandah at the rate of .

** Answer: **It is given that room is long and wide.

It is clear that it is rectangular shaped with

We know that the area of the rectangle is

-(i)

Now, when verandah of width is constructed all along outside the room then length and breadth of the room is

Area of the room after verandah of width is constructed

-(ii)

Area of verandah is (ii) - (i)

Therefore, area of verandah is

Now, the cost of cementing the floor of the verandah at the rate of is

Therefore, cost of cementing the floor of the verandah at the rate of is

** Question: ****5(i) ** A path wide is built along the border and inside a square garden of side . Find: the area of the path.

** Answer: ** Is is given that side of square garden is

We know that area of square is =

-(i)

Now, area of square garden without 1 m boarder is

-(ii)

Area of path is (i) - (ii)

Therefore, area of path is

**Question:**** 5(ii) ** A path wide is built along the border and inside a square garden of side . Find: the cost of planting grass in the remaining portion of the garden at the rate of

** Answer:** Is given that side of square garden is

We know that area of square is =

-(i)

Now, area of square garden without 1 m boarder is

-(ii)

Area of path is (i) - (ii)

Therefore, area of path is

Now, cost of planting grass in the remaining portion of the garden at the rate of is

Therefore, cost of planting grass in the remaining portion of the garden at the rate of is

** Question: ** ** 6 ** Two cross roads, each of width , cut at right angles through the centre of a rectangular park of length and breadth and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

** Answer: **

It is given that width of each road is and the length of rectangular park is and breadth is

Now, We know that area of rectangle is =

Area of total park is

-(i)

Area of road parallell to width of the park ( ABCD ) is

-(ii)

Area of road parallel to length of park ( PQRS ) is

-(iii)

The common area of both the roads ( KMLN ) is

-(iv)

Area of roads =

-(v)

Now, Area of the park excluding crossroads is =

** Question: **** 7(i) ** Through a rectangular field of length and breadth , two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is , find the area covered by the roads.

** Answer: **

It is given that the width of each road is and length of rectangular park is and breadth is

Now, We know that area of rectangle is =

Area of total park is

-(i)

Area of road parallell to width of the park ( ABCD ) is

-(ii)

Area of road parallel to length of park ( PQRS ) is

-(iii)

The common area of both the roads ( KMLN ) is

-(iv)

Area of roads =

Therefore, the area of road is

** Question: ** ** 7(ii) ** Through a rectangular field of length and breadth , two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is .find the cost of constructing the roads at the rate of .

** Answer: **

It is given that the width of each road is and the length of rectangular park is and breadth is

Now, We know that area of rectangle is =

Area of the total park is

-(i)

Area of road parallel to the width of the park ( ABCD ) is

-(ii)

Area of road parallel to the length of park ( PQRS ) is

-(iii)

The common area of both the roads ( KMLN ) is

-(iv)

Area of roads =

Now, the cost of constructing the roads at the rate of is

Therefore, the cost of constructing the roads at the rate of is

** Question: ** ** 8 ** Pragya wrapped a cord around a circular pipe of the radius (adjoining figure) and cut off the length required of the cord. Then she wrapped it around a square box of side (also shown). Did she have any cord left?

** Answer:** It is given that the radius of the circle is 4 cm

We know that circumference of circle =

And perimeter of the square is

Length of cord left is

Therefore, Length of cord left is

** Question:**** 9(i) ** The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: the area of the whole land.

** Answer: **We know that area rectangle is =

Area of rectangular land with length ** 10 m ** and width ** 5 m ** is

Therefore, area of rectangular land with length ** 10 m ** and width ** 5 m ** is

** Question: ****9(ii) ** The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: the area of the flower bed.

** Answer: **We know that area of circle is =

Area of flower bed with radius ** 2 m ** is

Therefore, area of flower bed with radius ** 2 m ** is

** Question: ** ** 9(iii) ** The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: the area of the lawn excluding the area of the flower bed.

** Answer: ** Area of the lawn excluding the area of the flower bed = Area of rectangular lawn - Area of flower bed

=

Therefore, area of the lawn excluding the area of the flower bed is

** Question: ****9(iv) ** The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: the circumference of the flower bed

** Answer: **We know that circumference of the circle is =

Circumference of the flower bed with radius ** 2 m ** is

Therefore, the circumference of the flower bed with radius ** 2 m ** is

** Question: ****10(i) ** In the following figure, find the area of the shaded portion:

** Answer: **Area of shaded portion = Area of the whole rectangle ( ABCD ) - Area of two triangles ( AFE and BCE)

Area of the rectangle with length 18 cm and width 10 cm is

Area of triangle AFE with base 10 cm and height 6 cm is

Area of triangle BCE with base 8 cm and height 10 cm is

Now, Area of the shaded portion is

** Question: ****10(ii) ** In the following figure, find the area of the shaded portion:

** Answer: **Area of shaded portion = Area of the whole square (PQRS) - Area of three triangles ( PTQ, STU and QUR )

Area of the square with side 20cm is

Area of triangle PTQ with base 10 cm and height 20 cm is

Area of triangle STU with base 10 cm and height 10 cm is

Area of triangle QUR with base 20 cm and height 10 cm is

Now, Area of the shaded portion is

** Question: ** ** 11 ** Find the area of the quadrilateral . Here, and

** Answer: **Area of quadrilateral ABCD = Area of triangle ABC + Area of tringle ADC

Area of triangle ABC with base 22 cm and height 3 cm is

Area of triangle ADX with base 22 cm and height 3 cm is

Therefore, the area of quadrilateral ABCD is =

**Perimeter And Area Class 7 Maths Chapter 11-Topics**

- Squares And Rectangles
- Triangles As Parts Of Rectangles
- Generalising For Other Congruent Parts Of Rectangles
- Area Of A Parallelogram
- Area Of A Triangle
- Circles
- Circumference Of A Circle
- Area Of Circle
- Conversion Of Units
- Applications

### NCERT Solutions for Class 7 Maths Chapter Wise

Chapter No. | Chapter Name |

Chapter 1 | Integers |

Chapter 2 | Fractions and Decimals |

Chapter 3 | Data Handling |

Chapter 4 | Simple Equations |

Chapter 5 | Lines and Angles |

Chapter 6 | The Triangle and its Properties |

Chapter 7 | Congruence of Triangles |

Chapter 8 | Comparing quantities |

Chapter 9 | Rational Numbers |

Chapter 10 | Practical Geometry |

Chapter 11 | Perimeter and Area |

Chapter 12 | Algebraic Expressions |

Chapter 13 | Exponents and Powers |

Chapter 14 | Symmetry |

Chapter 15 | Visualising Solid Shapes |

### NCERT Solutions for Class 7 Subject Wise

NCERT Solutions for Class 7 Maths |

NCERT Solutions for Class 7 Science |

### Some important point from NCERT solutions for Class 7th Maths chapter 11 Perimeter and Area

** Area of a triangle**: If the base length and height of a triangle are given

**The perimeter of the triangle:- ** Perimeter will be equal to the sum the sides of the triangle

a- First side of the triangle

b- Second side of the triangle

c- Third side of the triangle

** Area of Circles:- **

r-> Radius of the circle

** Circumference of Circle:- **

r-> Radius of the circle

** Area of a parallelogram: **

b-> base length

h-> height

Tip- You shouldn't just memorize the formulas, also understand the concept of how these formulas are derived. If you go through solutions of NCERT Solutions for Class 7 , you will understand all these concepts very easily.

** Happy Reading!!! **

**Also Check NCERT Books and NCERT Syllabus here:**

- NCERT Syllabus Class 7 Maths
- NCERT Books Class 7
- NCERT Syllabus Class 7