A wire of 32cm is bent to form the fig given below.if AB=BC=CD and APD is semicircle, find radius and area of given figure

Dear student,

Let the equal side be xcm
Clearly radius of the semi circle in the given  fig will be x/2 cm
Perimeter of fig. = 3 times the equal side + circumference of the semi circle
implies, 32=3x+(22/7)(x/2)
32 = 3x+(11/7)x
32=(32/7)x
x=7cm

Radius of circle = x/2 = 7/2 = 3.5cm

Area of the fig. = area of semi circle + area of square
                         = ((22/7)(x/2)2)/2 + x2 = (22/7)x(7/2)x(7/2)x(1/2)+7x7 = (77/4) + 49 = 19.25+49 =68.25 cm2.

Regards

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