The figure shows a triangle XYZ and 3 semicircles. If the shaded area of the semicircle, labelled V, is ¹₂ the unshaded area of the semicircle, labelled W, find the total shaded area. (Take π = 3.14)
Shaded part of Semicircle V : Unshaded part of Semicircle W : Area of shaded part of V and area of unshaded part of W
1 : 2 : 3

Area of Semicircle V
= ¹₂ x 3.14 x 6 x 6
= 56.52 cm²

Area of Semicircle W
= ¹₂ x 3.14 x 8 x 8 
= 100.48 cm²

Area of Triangle XYZ
= ¹₂ x 12 x 16
= 96 cm²

Total area of the figure
= 56.52 + 100.48 + 96
= 253 cm²

Area of the big semicircle
= ¹₂ x 3.14 x 10 x 10
= 157 cm²

Total area of the figure - Area of the big semicircle = 3 u

3 u = 253 - 157
3 u = 96 

1 u = 96 ÷ 3 = 32

Shaded part of Semicircle V
= 1 u
= 32 cm²

Unshaded part of Semicircle W
= 2 u
= 2 x 32
= 64 cm²

Shaded part of Semicircle W
= Area of Semicircle W - Area of unshaded part of Semicircle W
= 100.48 - 64
= 36.48 cm²

Total shaded areas
= Shaded area of Semicircle V + Shaded area of Semicircle W
= 32 + 36.48
= 68.48 cm²

Answer(s): 68.48 cm²