Question

From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the center as shown in Fig. Find the area of the remaining (shaded) portion of the square. (Use π = 22/7)

Answer 1

Given,

Side of the square = 8 cm

Radius of circle = 4.2 cm

Radius of the quadrant = 1.4 cm

Thus,

Area of the shaded potion = Area of square – Area of circle – 2 x Area of the quadrant

= side² – πr² – 2 x 1/2 πr²

= 8² – π(4.2)² – 2 x 1/2 π(1.4)²

= 64 – 22/7(4.2 x 4.2) – 22/7(1.4 x 1.4)

= 64 – 388.08/7 – 21.56/7

= 5.48 cm²