5. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.

5. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.

Solution:

Side of the square = 4 cm

Radius of the circle = 1 cm

Four quadrant of a circle are cut from corner and one circle of radius are cut from middle.

Area of square = (side)²= 4² = 16 cm²

Area of the quadrant = (πR²)/4 cm² = (22/7)×(1²)/4 = 11/14 cm²

∴ Total area of the 4 quadrants = 4 ×(11/14) cm² = 22/7 cm²

Area of the circle = πR² cm² = (22/7×1²) = 22/7 cm²

Area of the shaded region = Area of square – (Area of the 4 quadrants + Area of the circle)

= 16 cm²-(22/7) cm²+(22/7) cm²

= 68/7 cm²