Question

Four equal circles, each of radius 5 cm, touch each other as shown in Fig. Find the area included between them. (Take π = 3.14).

Answer 1

From the figure we can see that,

Side of the square = 10 cm

We know that area of the square = side x side = 10 x 10 = 100 cm²

Radius of the quarter circle = 5 cm

Area of the quarter circle = (π r²)/4

Area of 4 quarter circle = 4 × (πr²)/4

= πr² 

= 3.14 × (5)² 

= 78.5 cm²

Area included in the quarter circle = Area of the square – Area of the four quarter circles

Area included in them = (100 – 78.5) cm² 

= 21.5 cm²