The figure shows a triangle KLM and 3 semicircles. If the shaded area of the semicircle, labelled H, is ¹₃ the unshaded area of the semicircle, labelled J, find the total shaded area. (Take π = 3.14)
Shaded part of Semicircle H : Unshaded part of Semicircle J : Area of shaded part of H and area of unshaded part of J
1 : 3 : 4

Area of Semicircle H
= ¹₂ x 3.14 x 6 x 6
= 56.52 m²

Area of Semicircle J
= ¹₂ x 3.14 x 8 x 8 
= 100.48 m²

Area of Triangle KLM
= ¹₂ x 12 x 16
= 96 m²

Total area of the figure
= 56.52 + 100.48 + 96
= 253 m²

Area of the big semicircle
= ¹₂ x 3.14 x 10 x 10
= 157 m²

Total area of the figure - Area of the big semicircle = 4 u

4 u = 253 - 157
4 u = 96 

1 u = 96 ÷ 4 = 24

Shaded part of Semicircle H
= 1 u
= 24 m²

Unshaded part of Semicircle J
= 3 u
= 3 x 24
= 72 m²

Shaded part of Semicircle J
= Area of Semicircle J - Area of unshaded part of Semicircle J
= 100.48 - 72
= 28.48 m²

Total shaded areas
= Shaded area of Semicircle H + Shaded area of Semicircle J
= 24 + 28.48
= 52.48 m²

Answer(s): 52.48 m²