Radius of semicircle
= 10cm ÷ 2
= 5cm


Notice that the 4 semicircles overlap. When you add all 4 of them together, the shaded parts end up getting double counted. The unshaded area is also included.

Subtracting the area of the square from it removes these double counted parts , and also removes the unshaded area. leaving only the shaded part.


Area of shaded parts

= area of 4 semicircles - area of square

= area of 2 circles - area of square

= 2 x 3.14 x 5cm x 5cm - 10cm x 10cm

= 157cm² - 100cm²

= 57cm²

Alternatively, draw two diagonal lines , joining the opposite corners of the square.

You can see 4 identical triangles being formed. Each triangle has base 10cm long and height 5cm. (same as radius of circle)

Each of them are enclosed inside one semicircle.

When you cut away one triangle from one semicircle, you get two half-leaves.


Area of two half-leaves

= Area of semicircle - area of triangle

= ½ x 3.14 x 5cm x 5cm - ½ x 5 x 10cm

= 39.25cm² - 25cm²
= 14.25cm²

The shaded parts are made of eight half-leaves .

So area of shaded parts
= 14.25cm² x 4
= 57cm²