The figure is made up of a circle, a rectangle and 2 semicircles. VX, the diameter of the circle, is 30 m, VW is 24 m and WX is 18 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 VW
= 24 ÷ 2
= 12 m
Area of Semicircle VW
=
12 x 12 x 12 x 3.14
= 226.08 m
2
Radius of WX
= 18 ÷ 2
= 9 m
Area of Semicircle WX
=
12 x 9 x 9 x 3.14
= 127.17 m
2 Radius of VX
= 30 ÷ 2
= 15 m
Area of the semicircle VX = Radius VX
=
12 x 15 x 15 x 3.14
= 353.25 m
2 Total area of shaded parts
= 226.08 + 127.17 +
12 x 24 x 18 - 353.25
= 216 m
2 (b)
Length of Semicircle VW
=
12 x 3.14 x 24
= 37.68 m
Length of Semicircle WX
=
12 x 3.14 x 18
= 28.26 m
Length of Semicircle VX
=
12 x 3.14 x 30
= 47.1 m
Perimeter of shaded parts
= 37.68 + 28.26 + 47.1
= 226.08 m
Answer(s): (a) 216 m
2; (b) 226.08 m