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

Area of Semicircle F
= ¹₂ x 3.14 x 7.5 x 7.5
= 88.3125 cm²

Area of Semicircle G
= ¹₂ x 3.14 x 10 x 10 
= 157 cm²

Area of Triangle HJK
= ¹₂ x 15 x 20
= 150 cm²

Total area of the figure
= 88.3125 + 157 + 150
= 395.3125 cm²

Area of the big semicircle
= ¹₂ x 3.14 x 12.5 x 12.5
= 245.3125 cm²

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

4 u = 395.3125 - 245.3125
4 u = 150 

1 u = 150 ÷ 4 = 37.5

Shaded part of Semicircle F
= 1 u
= 37.5 cm²

Unshaded part of Semicircle G
= 3 u
= 3 x 37.5
= 112.5 cm²

Shaded part of Semicircle G
= Area of Semicircle G - Area of unshaded part of Semicircle G
= 157 - 112.5
= 44.5 cm²

Total shaded areas
= Shaded area of Semicircle F + Shaded area of Semicircle G
= 37.5 + 44.5
= 82 cm²

Answer(s): 82 cm²