The figure is made up of a circle, a rectangle and 2 semicircles. KM, the diameter of the circle, is 45 cm, KL is 36 cm and LM is 27 cm.

1. What is the total area of the shaded parts?
2. What is the total perimeter of the shaded parts? (Take π = 3.14)

(a)
Radius of KL
= 36 ÷ 2 
= 18 cm

Area of Semicircle KL
= ¹₂ x 18 x 18 x 3.14
= 508.68 cm²

Radius of LM
= 27 ÷ 2
= 13.5 cm

Area of Semicircle LM
= ¹₂ x 13.5 x 13.5 x 3.14
= 286.1325 cm²

Radius of KM
= 45 ÷ 2
= 22.5 cm

Area of the semicircle KM = Radius KM
= ¹₂ x 22.5 x 22.5 x 3.14
= 794.8125 cm²

Total area of shaded parts
= 508.68 + 286.1325 + ¹₂ x 36 x 27 - 794.8125
= 486 cm²

(b)
Length of Semicircle KL
= ¹₂ x 3.14 x 36
= 56.52 cm

Length of Semicircle LM
= ¹₂ x 3.14 x 27
= 42.39 cm

Length of Semicircle KM
= ¹₂ x 3.14 x 45
= 70.65 cm

Perimeter of shaded parts
= 56.52 + 42.39 + 70.65 
= 508.68 cm

Answer(s): (a) 486 cm²; (b) 508.68 cm