NCERT Exemplar solutions for Mathematics [English] Class 7 chapter 9 - Perimeter and Area [Latest edition]

Observe the shapes 1, 2, 3 and 4 in the figures. Which of the following statements is not correct?

A rectangular piece of dimensions 3 cm × 2 cm was cut from a rectangular sheet of paper of dimensions 6 cm × 5 cm (see the figure). Area of remaining sheet of paper is ______.

36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is ______.

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is ______.

Area of the circle obtained in 196 m² is ______.

Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14 cm × 11 cm, then radius of the circle is ______.

Area of shaded portion in the figure given below is ______.

Area of parallelogram ABCD (see the figure) is not equal to ______.

Area of triangle MNO in the figure is ______.

Ratio of area of ∆MNO to the area of parallelogram MNOP in the same figure is ______.

Ratio of areas of ∆MNO, ∆MOP and ∆MPQ in the given figure is ______.

In the given figure, EFGH is a parallelogram, altitudes FK and FI are 8 cm and 4 cm respectively. If EF = 10 cm, then area of EFGH is ______.

In reference to a circle the value of π is equal to ______.

Circumference of a circle is always ______.

Area of triangle PQR is 100 cm² as shown in the below figure. If altitude QT is 10 cm, then its base PR is ______.

In the given figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is ______.

In the given figure, ΔMNO is a right-angled triangle. Its legs are 6 cm and 8 cm long. Length of perpendicular NP on the side MO is ______.

Area of a right-angled triangle is 30 cm². If its smallest side is 5 cm, then its hypotenuse is ______.

Circumference of a circle of diameter 5 cm is ______.

Circumference of a circle disc is 88 cm. Its radius is ______.

Length of tape required to cover the edges of a semicircular disc of radius 10 cm is ______.

Area of circular garden with diameter 8 m is ______.

Area of a circle with diameter ‘m’ radius ‘n’ and circumference ‘p’ is ______.

A table top is semicircular in shape with diameter 2.8 m. Area of this table top is ______.

If 1 m² = x mm², then the value of x is ______.

If p squares of each side 1 mm makes a square of side 1 cm, then p is equal to ______.

12 m² is the area of ______.

If each side of a rhombus is doubled, how much will its area increase?

If the sides of a parallelogram are increased to twice its original lengths, how much will the perimeter of the new parallelogram?

If radius of a circle is increased to twice its original length, how much will the area of the circle increase?

What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

What is the radius of the largest circle that can be cut out of the rectangle measuring 10 cm in length and 8 cm in breadth?

The perimeter of the figure ABCDEFGHIJ is ______.

The circumference of a circle whose area is 81 πr², is ______.

The area of a square is 100 cm². The circumference (in cm) of the largest circle cut of it is ______.

If the radius of a circle is tripled, the area becomes ______.

The area of a semicircle of radius 4r is ______.

Perimeter of a regular polygon = length of one side × ______.

If a wire in the shape of a square is rebent into a rectangle, then the ______ of both shapes remain same, but ______ may varry.

Area of the square MNOP of the given figure is 144 cm². Area of each triangle is ______.

In the given figure, area of parallelogram BCEF is ________ cm² where ACDF is a rectangle.

To find area, any side of a parallelogram can be chosen as ______ of the parallelogram.

Perpendicular dropped on the base of a parallelogram from the opposite vertex is known as the corresponding ______ of the base.

The distance around a circle is its ______.

Ratio of the circumference of a circle to its diameter is denoted by symbol ______.

If area of a triangular piece of cardboard is 90 cm², then the length of altitude corresponding to 20 cm long base is ______ cm.

Value of π is ______ approximately.

Circumference ‘C’ of a circle can be found by multiplying diameter ‘d’ with ______.

Circumference ‘C’ of a circle is equal to 2π × ______.

1 m² = ______ cm².

1 cm² = ______ mm².

1 hectare = ______ m².

Area of a triangle = `1/2` base × ______.

1 km² = ______ m².

Area of a square of side 6 m is equal to the area of ______ squares of each side 1 cm.

10 cm² = ______ m².

In the given figure, perimeter of (ii) is greater than that of (i), but its area is smaller than that of (i).

(i)	(ii)

In the given figure, Area of (i) is the same as the area of (ii)

(i)	(ii)

In the given figure, perimeter of (ii) is the same as (i).

(i)	(ii)

In the given figure, if (ii) is divided into squares of unit length, then its area is 13 unit squares.

(ii)

In the given figure, perimeter of (ii) is 18 units.

(ii)

If perimeter of two parallelograms are equal, then their areas are also equal.

All congruent triangles are equal in area.

All parallelograms having equal areas have same perimeters.

Observe all the four triangles FAB, EAB, DAB and CAB as shown in the given figure. 

1. All triangles have the same base and the same altitude.
2. All triangles are congruent.
3. All triangles are equal in area.
4. All triangles may not have the same perimeter.

In the given figure, ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of ΔACD.

Triangles having the same base have equal area.

Ratio of circumference of a circle to its radius is always 2π:I.

5 hectare = 500 m²

An increase in perimeter of a figure always increases the area of the figure.

Two figures can have the same area but different perimeters.

Out of two figures if one has larger area, then its perimeter need not to be larger than the other figure.

A hedge boundary needs to be planted around a rectangular lawn of size 72 m × 18 m. If 3 shrubs can be planted in a metre of hedge, how many shrubs will be planted in all?

People of Khejadli village take good care of plants, trees and animals. They say that plants and animals can survive without us, but we can not survive without them. Inspired by her elders Amrita marked some land for her pets (camel and ox) and plants. Find the ratio of the areas kept for animals and plants to the living area.

The perimeter of a rectangle is 40 m. Its length is four metres less than five times its breadth. Find the area of the rectangle.

A wall of a room is of dimensions 5 m × 4 m. It has a window of dimensions 1.5 m × 1 m and a door of dimensions 2.25 m × 1 m. Find the area of the wall which is to be painted.

Rectangle MNOP is made up of four congruent rectangles (Figure). If the area of one of the rectangles is 8 m² and breadth is 2 m, then find the perimeter of MNOP.

In the given figure, area of ∆AFB is equal to the area of parallelogram ABCD. If altitude EF is 16 cm long, find the altitude of the parallelogram to the base AB of length 10 cm. What is the area of ∆DAO, where O is the midpoint of DC?

Ratio of the area of ∆WXY to the area of ∆WZY is 3:4 in the given figure. If the area of ∆WXZ is 56 cm² and WY = 8 cm, find the lengths of XY and YZ.

Rani bought a new field that is next to one she already owns in the given figure. This field is in the shape of a square of side 70 m. She makes a semi-circular lawn of maximum area in this field.

1. Find the perimeter of the lawn.
2. Find the area of the square field excluding the lawn.

In the given figure, find the area of parallelogram ABCD, if the area of shaded triangle is 9 cm².

Pizza factory has come out with two kinds of pizzas. A square pizza of side 45 cm costs ₹ 150 and a circular pizza of diameter 50 cm costs ₹ 160 (Figure). Which pizza is a better deal?

Three squares are attached to each other as shown in the figure given below. Each square is attached at the mid-point of the side of the square to its right. Find the perimeter of the complete figure.

In the following figure, ABCD is a square with AB = 15 cm. Find the area of the square BDFE.

In the given figures, perimeter of ΔABC = perimeter of ΔPQR. Find the area of ΔABC.

Altitudes MN and MO of parallelogram MGHK are 8 cm and 4 cm long respectively in the below figure. One side GH is 6 cm long. Find the perimeter of MGHK.

In the given figure, area of ΔPQR is 20 cm² and area of ΔPQS is 44 cm². Find the length RS, if PQ is perpendicular to QS and QR is 5 cm.

Area of an isosceles triangle is 48 cm². If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.

Perimeter of a parallelogram shaped land is 96 m and its area is 270 square metres. If one of the sides of this parallelogram is 18 m, find the length of the other side. Also, find the lengths of altitudes l and m in the given figure.

Area of a triangle PQR right-angled at Q is 60 cm² in the figure. If the smallest side is 8 cm long, find the length of the other two sides.

In the given figure, a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles.

Find the area of a square inscribed in a circle whose radius is 7 cm in the below figure.

[Hint: Four right-angled triangles joined at right angles to form a square]

Find the area of the shaded portion in a circle whose radius is 7 cm.

Find the area enclosed by the following figure:

Find the area enclosed by the following figure:

Find the area enclosed by the following figure:

Find the area enclosed by the following figure:

Find the area of the shaded region:

Find the area of the shaded region:

A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in the below figure:

Does the perimeter change? If it does change, by how much does it increase or decrease?

A large square is made by arranging a small square surrounded by four congruent rectangles as shown in the given figure. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.

ABCD is a parallelogram in which AE is perpendicular to CD as shown in the given figure. Also, AC = 5 cm, DE = 4 cm and area of ΔAED = 6 cm². Find the perimeter and area of parallelogram ABCD.

Ishika has designed a small oval race track for her remote control car. Her design is shown in the given figure. What is the total distance around the track? Round your answer to the nearest whole centimetre.

A table cover of dimensions 3 m 25 cm × 2 m 30 cm is spread on a table. If 30 cm of the table cover is hanging all around the table, find the area of the table cover which is hanging outside the top of the table. Also find the cost of polishing the table top at ₹ 16 per square metre.

The dimensions of a plot are 200 m × 150 m. A builder builds 3 roads which are 3 m wide along the length on either side and one in the middle. On either side of the middle road he builds houses to sell. How much area did he get for building the houses?

A room is 4.5 m long and 4 m wide. The floor of the room is to be covered with tiles of size 15 cm by 10 cm. Find the cost of covering the floor with tiles at the rate of ₹ 4.50 per tile.

Find the total cost of wooden fencing around a circular garden of diameter 28 m, if 1 m of fencing costs ₹ 300.

Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?

How much distance, in metres, a wheel of 25 cm radius will cover if it rotates 350 times?

A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.

A carpet of size 5 m × 2 m has 25 cm wide red border. The inner part of the carpet is blue in colour (see the figure). Find the area of blue portion. What is the ratio of areas of red portion to blue portion?

Use the following figure, showing the layout of a farm house:

1. What is the area of land used to grow hay?
2. It costs ₹ 91 per m² to fertilise the vegetable garden. What is the total cost?
3. A fence is to be enclosed around the house. The dimensions of the house are 18.7 m × 12.6 m. At least how many metres of fencing are needed?
4. Each banana tree required 1.25 m² of ground space. How many banana trees can there be in the orchard?

Study the layout given in the figure and answer the questions:

1. Write an expression for the total area covered by both the bedrooms and the kitchen.
2. Write an expression to calculate the perimeter of the living room.
3. If the cost of carpeting is ₹ 50/m², write an expression for calculating the total cost of carpeting both the bedrooms and the living room.
4. If the cost of tiling is ₹ 30/m², write an expression for calculating the total cost of floor tiles used for the bathroom and kitchen floors.
5. If the floor area of each bedroom is 35 m², then find x.

A 10 m long and 4 m wide rectangular lawn is in front of a house. Along its three sides a 50 cm wide flower bed is there as shown in the given figure. Find the area of the remaining portion.

A school playground is divided by a 2 m wide path which is parallel to the width of the playground, and a 3 m wide path which is parallel to the length of the ground in the given figure. If the length and width of the playground are 120 m and 80 m respectively, find the area of the remaining playground.

In a park of dimensions 20 m × 15 m, there is a L shaped 1 m wide flower bed as shown in the figure. Find the total cost of manuring for the flower bed at the rate of Rs 45 per m².

Dimensions of a painting are 60 cm × 38 cm. Find the area of the wooden frame of width 6 cm around the painting as shown in given figure.

A design is made up of four congruent right triangles as shown in the given figure. Find the area of the shaded portion.

A square tile of length 20 cm has four quarter circles at each corner as shown in figure (i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile in figure (ii). If the circle touches all four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take, π = 3.14)

(i)	(ii)

A rectangular field is 48 m long and 12 m wide. How many right triangular flower beds can be laid in this field, if sides including the right angle measure 2 m and 4 m, respectively?

Ramesh grew wheat in a rectangular field that measured 32 metres long and 26 metres wide. This year he increased the area for wheat by increasing the length but not the width. He increased the area of the wheat field by 650 square metres. What is the length of the expanded wheat field?

In the given figure, triangle AEC is right-angled at E, B is a point on EC, BD is the altitude of triangle ABC, AC = 25 cm, BC = 7 cm and AE = 15 cm. Find the area of triangle ABC and the length of DB.

Calculate the area of shaded region in the given figure, where all of the short line segments are at right angles to each other and 1 cm long.

The plan and measurement for a house are given in the figure. The house is surrounded by a path 1 m wide.

Find the following:

1. Cost of paving the path with bricks at rate of ₹ 120 per m².
2. Cost of wooden flooring inside the house except the bathroom at the cost of ₹ 1200 per m².
3. Area of Living Room.

Architects design many types of buildings. They draw plans for houses, such as the plan shown in the following figure:

An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding costs ₹ 500/metre.

1. Find how much moulding will be needed for each room.
   (i) family room
   (ii) living room
   (iii) dining room
   (iv) bedroom 1
   (v) bedroom 2
2. The carpet costs ₹ 200/m². Find the cost of carpeting each room.
3. What is the total cost of moulding for all the five rooms.

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the midpoints of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

4 squares each of side 10 cm have been cut from each corner of a rectangular sheet of paper of size 100 cm × 80 cm. From the remaining piece of paper, an isosceles right triangle is removed whose equal sides are each of 10 cm length. Find the area of the remaining part of the paper.

A dinner plate is in the form of circle. A circular region encloses a beautiful design as shown in the given figure. The inner circumference is 352 mm and outer is 396 mm. Find the width of circular design.

The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution. (Take π = 3.14)

A photograph of Billiard/Snooker table has dimensions as `1/10`th of its actual size as shown in the given figure:

The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of ₹ 200 per m². Find the cost of polishing.