Contents

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

### Chapter 11 Perimeter and Area Exercise 11.1

**Question 1.**

The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find

**(i)** its area

**(ii)** the cost of the land if 1 m^{2} of the land costs ₹ 10,000.

**Solution:
**

**(i)**For a rectangular piece of land,

Length = 500 m

Breadth = 300 m

∴ Area of the rectangular piece of land = Length × Breadth , = 500 × 300 m

^{2}= 150,000 m

^{2}

**(ii)** 1 m^{2} of the land costs = ₹ 10,000

∵ 150,000 m^{2} of the land costs = ₹ 10,000 × 150,000 = ₹ 1,500,000,000.

**Question 2.**

Find the area of a square park whose perimeter is 320 m.

**Solution:**

We have, perimeter of a square park = 320 m

∴ Side of the square park = ([late×]\frac { 320 }{ 4 } [/late×]) m = 80 m

∴ Area of square park = (Side)^{2 }= (80)^{2} m^{2} = 6400 m^{2}

**Question 3.**

Find the breadth of a rectangular plot of land, if its area is 440 m^{2} and the length is 22 m. Also find its perimeter.

**Solution:**

Let the breadth of the rectangular plot of land be b.

It is given that length of the plot = 22 m

and the area of the plot = 440 m^{2
}

**Question 4.**

The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also, find the area.

**Solution:**

Let the breadth of the rectangular sheet be b cm.

It is given that its length is 35 cm and perimeter is 100 cm.

**Question 5.**

The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

**Solution:
**

**Question 6.**

A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. 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?

**Solution:
**

Hence, the measure of the side of the square is 31 cm and the square shape encloses more area.

**Question 7.**

The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.

**Solution:
**

**Question 8.**

A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m. Find the cost of white washing the wall, if the rate of white washing the wall is ₹ 20 per m^{2}.

**Solution:
**

### Chapter 11 Perimeter and Area Exercise 11.2

**Question 1.**

Find the area of each of the following parallelograms :

**Solution:**

**(a)** Area of the parallelogram = base × height = (7 × 4) cm^{2} = 28 cm^{2}

**(b)** Area of the parallelogram = base × height = (5 × 3) cm^{2} = 15 cm^{2}

**(c)** Area of the karallelogram = base × height = (2.5 × 3.5) cm^{2} = 8.75 cm^{2}

**(d)** Area of the parallelogram = base × height = (5 × 4.8) cm^{2} = 24 cm^{2}

**(e)** Area of the parallelogram = base × height = (2 × 4.4) cm2 = 8.8 cm^{2}

**Question 2.**

Find the area of each of the following triangles :

**Solution:
**

**Question 3.**

Find the missing values :

**Solution:**

We know that

Area of a parallelogram = Base × Height

Therefore, the missing values are calculated as shown :

**Question 4.**

Find the missing values :

**Solution:
**

**Question 5.**

PQRS is a parallelogram (in the given figure). QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find

**(a)** the area of the parallelogram PQRS.

**(b)** QN, if PS = 8 cm.

**Solution:
**

**Question 6.**

DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD (in the given figure). If the area of the parallelogram is 1470 cm^{2}, AB = 35 cm, AD = 49 cm, find the length of BM and DL.

**Solution:
**

**Question 7.**

∆ ABC is right angled at A (in the given figure). AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, find the area of ∆ABC. Also find the length of AD.

**Solution:
**

**Question 8.**

∆ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm (in the given figure). The height AD from A to BC is 6 cm. Find the area of A ABC. What will be the height from C to AB i.e., CE ?

**Solution:
**

### Chapter 11 Perimeter and Area Exercise 11.3

**Question 1.**

Find the circumference of the circles with the following radius : ( Take π \(\frac { 22 }{ 7 } \))

**(a)** 14 cm

**(b)** 28 mm

**(c)** 21 cm

**Solution:
**

**Question 2.**

Find the area of the following circles, given that :

**(a)** radius = 14 mm (Take π = \(\frac { 22 }{ 7 } \))

**(b)** diameter = 49 m

**(c)** radius = 5cm

**Solution:
**

**Question 3.**

If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 4.**

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs ₹ 4 per metre (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 5.**

From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)

**Solution:**

Here, Outer radius, r = 4 cm

Inner radius, r = 3 cm

Area of the remaining sheet = Outer area – Inner area

= π (R^{2} – r^{2}) = 3.14 (4^{2} – 3^{2}) cm^{2}

= 3.14 (16 – 9) cm^{2}

= 3.14 × 7 cm^{2} = 21.98 cm^{2}

**Question 6.**

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also its cost if one metre of the lace costs ₹ 15. (Take π = 3.14)

**Solution:
**

**Question 7.**

Find the perimeter of the adjoining figure, which is a semicircle including its diameter.

**Solution:
**

**Question 8.**

Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹ 15/m^{2} (Take π = 3.14)

**Solution:
**

**Question 9.**

Shazli took a wire of length 44 cm 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 of the square ? (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 10.**

From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the adjoining figure). Find the area of the remaining sheet (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 11.**

A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)

**Solution:**

Area of the square aluminium sheet = (6)^{2} cm^{2} = 36 cm^{2}

Area of the circle cut out from the sheet = (3.14 × 2 × 2) cm^{2} = 12.56 cm^{2}

Area of the sheet left over = (36 – 12.56) cm^{2} = 23.44 cm^{2}

**Question 12.**

The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)

**Solution:
**

**Question 13.**

A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)

**Solution:
**

**Question 14.**

A circular flower garden has an area of 314 m^{2}. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)

**Solution:**

Circular area of the sprinkler = πr^{2}

= 3.14 × 12 × 12

=3.14 × 144 = 452.16 m^{2}

Area of the circular flower garden = 314 m^{2}

Since, area of the circular flower garden is smaller than by sprinkler. Therefore, the sprinkler will water the entire garden.

**Question 15.**

Find the circumference of the inner and the outer circles, shown in the adjoining figure. (Take π = 3.14)

**Solution:
**

**Question 16.**

How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = \(\frac { 22 }{ 7 } \))

**Solution:
**

**Question 17.**

The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour? (Take π = 3.14)

**Solution:**

We know that the minute hand describes one complete revolution in one hour.

∴ Distance covered by its tip

= Circumference of the circle of radius 15 cm

= (2 × 3.14 × 15) cm

= 94.2 cm

### Chapter 11 Perimeter and Area Exercise 11.4

**Question 1.**

A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

**Solution:
**

**Question 2.**

A 3 m wide path runs outside and around a rectangular-park of length 125 m and the breadth 65 m. Find the area of the path.

**Solution:
**

**Question 3.**

A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.

**Solution:
**

**Question 4.**

A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find :

**(i)** the area of the verandah,

**(ii)** the cost of cementing the floor of the verandah at the rate of ₹ 200 per m^{2}.

**Solution:
**

**Question 5.**

A path 1 m wide is built along the border inside a square garden of side 30 m. Find :

**(i)** the area of the path,

**(ii)** the cost of planting grass in the remaining portion of the garden at the rate of ₹ 40 per m^{2}.

**Solution:
**

**Question 6.**

Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m 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.

**Solution:
**

**Question 7.**

Through a rectangular field of length 90 m and breadth 60 m, 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 3 m, find :

**(i)** the area covered by the roads,

**(ii)** the cost of constructing the roads at the rate of ₹ 110 per m^{2}.

**Solution:
**

**Question 8.**

Pragya wrapped a cord around a circular pipe of radius 4 cm (adjoining figure) and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (π = 3.14)

**Solution:
**

**Question 9.**

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find :

**(i)** the area of the Whole land,

**(ii)** the area of the flower bed,

**(iii**) the area of the lawn excluding the area of the flower bed,

**(iv)** the circumference of the flower bed.

**Solution:
**

**Question 10.**

In the following figures, find the area of the shaded portions :

**Solution:
**

**Question 11.**

Find the area of the quadrilateral ABCD.

Here, AC = 22 cm,

BM = 3 cm,

DN = 3 cm, and BM ⊥ AC, DN ⊥ AC.

**Solution:
**