NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 9: Perimeter and Area

Problems and Solutions

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.