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

Area of Semicircle S
= ¹₂ x 3.14 x 3 x 3
= 14.13 cm²

Area of Semicircle T
= ¹₂ x 3.14 x 4 x 4 
= 25.12 cm²

Area of Triangle UVW
= ¹₂ x 6 x 8
= 24 cm²

Total area of the figure
= 14.13 + 25.12 + 24
= 63.25 cm²

Area of the big semicircle
= ¹₂ x 3.14 x 5 x 5
= 39.25 cm²

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

4 u = 63.25 - 39.25
4 u = 24 

1 u = 24 ÷ 4 = 6

Shaded part of Semicircle S
= 1 u
= 6 cm²

Unshaded part of Semicircle T
= 3 u
= 3 x 6
= 18 cm²

Shaded part of Semicircle T
= Area of Semicircle T - Area of unshaded part of Semicircle T
= 25.12 - 18
= 7.12 cm²

Total shaded areas
= Shaded area of Semicircle S + Shaded area of Semicircle T
= 6 + 7.12
= 13.12 cm²

Answer(s): 13.12 cm²