The figure is made up of a circle, a rectangle and 2 semicircles. UW, the diameter of the circle, is 45 m, UV is 36 m and VW is 27 m.
- 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
= 36 ÷ 2
= 18 m
Area of Semicircle UV
=
12 x 18 x 18 x 3.14
= 508.68 m
2
Radius of VW
= 27 ÷ 2
= 13.5 m
Area of Semicircle VW
=
12 x 13.5 x 13.5 x 3.14
= 286.1325 m
2 Radius of UW
= 45 ÷ 2
= 22.5 m
Area of the semicircle UW = Radius UW
=
12 x 22.5 x 22.5 x 3.14
= 794.8125 m
2 Total area of shaded parts
= 508.68 + 286.1325 +
12 x 36 x 27 - 794.8125
= 486 m
2 (b)
Length of Semicircle UV
=
12 x 3.14 x 36
= 56.52 m
Length of Semicircle VW
=
12 x 3.14 x 27
= 42.39 m
Length of Semicircle UW
=
12 x 3.14 x 45
= 70.65 m
Perimeter of shaded parts
= 56.52 + 42.39 + 70.65
= 508.68 m
Answer(s): (a) 486 m
2; (b) 508.68 m