The figure is made up of a circle, a rectangle and 2 semicircles. WY, the diameter of the circle, is 60 cm, WX is 48 cm and XY is 36 cm.
- What is the total area of the shaded parts?
- What is the total perimeter of the shaded parts? (Take π = 3.14)
(a)
Radius of WX
= 48 ÷ 2
= 24 cm
Area of Semicircle WX
=
12 x 24 x 24 x 3.14
= 904.32 cm
2
Radius of XY
= 36 ÷ 2
= 18 cm
Area of Semicircle XY
=
12 x 18 x 18 x 3.14
= 508.68 cm
2 Radius of WY
= 60 ÷ 2
= 30 cm
Area of the semicircle WY = Radius WY
=
12 x 30 x 30 x 3.14
= 1413 cm
2 Total area of shaded parts
= 904.32 + 508.68 +
12 x 48 x 36 - 1413
= 864 cm
2 (b)
Length of Semicircle WX
=
12 x 3.14 x 48
= 75.36 cm
Length of Semicircle XY
=
12 x 3.14 x 36
= 56.52 cm
Length of Semicircle WY
=
12 x 3.14 x 60
= 94.2 cm
Perimeter of shaded parts
= 75.36 + 56.52 + 94.2
= 904.32 cm
Answer(s): (a) 864 cm
2; (b) 904.32 cm