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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.


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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