# 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 π= 3.14)

**Solution:**

(i) Given, a square tile of length 20 cm has four quarter circles at each corner.

We have to find the area of the shaded region.

Area of shaded region = area of square tile - area of 4 quarter circles

= area of square tile - area of circle

__Area of square__ = (side)²

Area of square tile = (20)² = 400 cm²

The length of the side of square is equal to the diameter of the circle

Diameter = 20 cm

Radius = 20/2 = 10 cm

__Area of circle__ = πr²

= (3.14)(10)²

= 3.14(100)

= 314 cm²

Area of shaded region = 400 - 314 = 86 cm² --------------- (1)

(ii) Another square tile of length 20 cm has a circle in the centre of the tile.

We have to find the area of the shaded region.

Area of shaded region = area of square tile - area of circle

Area of square = (side)²

Area of square tile = (20)² = 400 cm²

The length of the side of the square is equal to the diameter of the circle.

Diameter = 20 cm

Radius = 20/2 = 10 cm

Area of circle = πr²

= (3.14)(10)²

= 3.14(100)

= 314 cm²

Area of shaded region = 400 - 314

= 86 cm² ------------------------- (2)

From (1) and (2),

We observe that both (i) and (ii) have the same area of the shaded region.

**✦ Try This: **If the circumference of a circle is increased by 50%, then by how much percent is the area of the circle increased?

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 11

**NCERT Exemplar Class 7 Maths Chapter 9 Problem 119**

## 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 π = 3.14)

**Summary:**

A square tile of length 20 cm has four quarter circles at each corner as shown in Fig. 9.64(i). The area of the shaded portion is 86 cm². Another tile with the 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, the area of the shaded portion is 86 cm². The area of the shaded portion will be equal in both the cases.

**☛ Related Questions:**

- A rectangular field is 48 m long and 12 m wide. How many right triangular flower beds can be laid in . . . .
- Ramesh grew wheat in a rectangular field that measured 32 metres long and 26 metres wide. This year . . . .
- In Fig. 9.65, triangle AEC is right-angled at E, B is a point on EC, BD is the altitude of triangle . . . .

visual curriculum