NCERT Exemplar Solutions
Class 7 - Mathematics

Unit 9: Perimeter and Area

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 vary.

Area of the square MNOP of Fig. 9.24 is 144 cm². Area of each triangle is ________.

In Fig. 9.25, 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 = ½ 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.

57. In Fig. 9.26, perimeter of (ii) is greater than that of (i), but its area is smaller than that of (i).

58. In Fig. 9.27,

(a) area of (i) is the same as the area of (ii).

(b) Perimeter of (ii) is the same as (i).

(c) If (ii) is divided into squares of unit length, then its area is 13 unit squares.

(d) Perimeter of (ii) is 18 units.

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.

All triangles have the same base and the same altitude.

All triangles are congruent.

All triangles are equal in area.

All triangles may not have the same perimeter.

In Fig. 9.29 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 triangle ACD.

Triangles having the same base have equal area.

Ratio of circumference of a circle to its radius is always 2π : 1.

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 be larger than the other figure.

A circle with radius 16 cm is cut into four equal parts and rearranged. Does the perimeter change?

Table cover dimensions 3.25 m × 2.30 m, 30 cm overhang. Find hanging area and cost of polishing.

Plot dimensions 200 m × 150 m, 3 roads of 3 m width. Find buildable area.

Room = 4.5 × 4 m. Tiles = 15 × 10 cm. Cost = ₹4.5 per tile.

Circular garden diameter 28 m. Fencing cost ₹300 per m.

Wire bent into circle of radius 14 cm then into rectangle length 24 cm.

Wheel radius 25 cm. Distance covered in 350 rotations?

Circular pond surrounded by path width 2 m. Outer circumference = 44 m.

Carpet = 5 m × 2 m, border 25 cm. Find blue area and ratio red:blue.

A design is made up of four congruent right triangles as shown in Fig. 9.63. Find the area of the shaded portion.

A square tile of length 20 cm has four quarter circles at each corner as shown in Fig. 9.64(i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [Fig. 9.64(ii)]. If the circle touches all the four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take \(\pi = 3.14\))

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 m long and 26 m 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 m². What is the length of the expanded wheat field?

In Fig. 9.65, 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.

How many pieces of 1.5 cm × 2 cm chocolate can be cut from a 18 cm × 18 cm sheet of chocolate?

Calculate the area of shaded region in Fig. 9.66, 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 Fig. 9.67. The house is surrounded by a path 1 m wide. Find the following: (i) Cost of paving the path with bricks at rate of ₹120 per m². (ii) Cost of wooden flooring inside the house except the bathroom at the cost of ₹1200 per m². (iii) Area of Living Room.

Architects design many types of buildings. They draw plans for houses, such as the plan shown in Fig. 9.68. An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding costs ₹500/metre.

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in Fig. 9.69. 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 a circle. A circular region encloses a beautiful design as shown in Fig. 9.70. 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 \(\pi = 3.14\))

A photograph of Billiard/Snooker table has dimensions as \(\tfrac{1}{10}\)th of its actual size as shown in Fig. 9.71: 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.