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

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

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

Area of Triangle JKL
= 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 G
= 1 u
= 24 m²

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

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

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

Answer(s): 52.48 m²