# Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces

**Solution:**

Given, four circular cardboard pieces of radii 7 cm are placed on a paper such that each piece touches the other two pieces.

We have to find the area of the portion enclosed between these pieces.

From the figure,

A, B, C and D are the four circular cardboard pieces of radii 7 cm.

On joining the centres, A, B, C and D form a square.

The side of square = 7 + 7 = 14 cm

Thus, the sides AB = AC = BD = CD = 14 cm

Area of the portion enclosed between these cardboard pieces = area of square - area of 4 sectors.

Area of square = (side)²

= (14)²

= 196 cm²

We know that the angle between the two adjacent sides of a square is 90°

So ∠A = ∠B = ∠C = ∠D = 90°

Area of sector = πr²θ/360°

Area of sector with angle A = (22/7)(7)²(90°/360°)

= (22)(7)(1/4)

= 154/4

= 38.5 cm²

Area of 4 sectors = 4(area of sector with angle A)

= 4(38.5)

= 154 cm²

Area of shaded region = 196 - 154

= 42 cm²

Therefore, the area of the shaded region is 42 cm².

**✦ Try This: **Four circular cardboard pieces of radii 4 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 9**

## Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces

**Summary:**

Four circular cardboard pieces of radii 7 cm are placed on a piece of paper in such a way that each piece touches the other two pieces. The area of the portion enclosed between these pieces is 42 cm²

**☛ Related Questions:**

- On a square cardboard sheet of area 784 cm² , four congruent circular plates of maximum size are pla . . . .
- Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm . . . .
- All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle i . . . .

visual curriculum