Question

Square ABCD has side length a. Half circles with
diameters BC and CD are drawn inside the
square. Find the area of the
shaded region.

Answer 1

The area of the shaded region is $0.215a^2$

Area of composite objects

The area of the shaded region is expressed according to the formula:

• $A = A_s - A_c$

Get the area of the square As

As = a²

$A_c = \pi (0.5a)^2\\ A_c = 0.785a^2$

Take the difference in the areas

Area of the shaded part = $a^2-0.785a^2$

Area of the shaded part = $0.215a^2$

Hence the area of the shaded region is $0.215a^2$

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