Question

# Question 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.

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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 is cut from middle. Area of square =(side)2=42=16 cm2 Area of the quadrant =(πR2)4cm2=(227×12)4=1114cm2 ∴ Total area of the 4 quadrants =4×(1114)cm2=227cm2 Area of the circle =πR2cm2=(227×12)=227cm2 Area of the shaded region = Area of square - (Area of the 4 quadrants + Area of the circle) =16cm2−(227+227)cm2 =687cm2

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