The figure is made up of a circle, a rectangle and 2 semicircles. UW, the diameter of the circle, is 20 cm, UV is 16 cm and VW is 12 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 UV
= 16 ÷ 2
= 8 cm
Area of Semicircle UV
=
12 x 8 x 8 x 3.14
= 100.48 cm
2
Radius of VW
= 12 ÷ 2
= 6 cm
Area of Semicircle VW
=
12 x 6 x 6 x 3.14
= 56.52 cm
2 Radius of UW
= 20 ÷ 2
= 10 cm
Area of the semicircle UW = Radius UW
=
12 x 10 x 10 x 3.14
= 157 cm
2 Total area of shaded parts
= 100.48 + 56.52 +
12 x 16 x 12 - 157
= 96 cm
2 (b)
Length of Semicircle UV
=
12 x 3.14 x 16
= 25.12 cm
Length of Semicircle VW
=
12 x 3.14 x 12
= 18.84 cm
Length of Semicircle UW
=
12 x 3.14 x 20
= 31.4 cm
Perimeter of shaded parts
= 25.12 + 18.84 + 31.4
= 100.48 cm
Answer(s): (a) 96 cm
2; (b) 100.48 cm