The figure is made up of a circle, a rectangle and 2 semicircles. VX, the diameter of the circle, is 75 m, VW is 60 m and WX is 45 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
= 60 ÷ 2
= 30 m
Area of Semicircle VW
=
12 x 30 x 30 x 3.14
= 1413 m
2
Radius of WX
= 45 ÷ 2
= 22.5 m
Area of Semicircle WX
=
12 x 22.5 x 22.5 x 3.14
= 794.8125 m
2 Radius of VX
= 75 ÷ 2
= 37.5 m
Area of the semicircle VX = Radius VX
=
12 x 37.5 x 37.5 x 3.14
= 2207.8125 m
2 Total area of shaded parts
= 1413 + 794.8125 +
12 x 60 x 45 - 2207.8125
= 1350 m
2 (b)
Length of Semicircle VW
=
12 x 3.14 x 60
= 94.2 m
Length of Semicircle WX
=
12 x 3.14 x 45
= 70.65 m
Length of Semicircle VX
=
12 x 3.14 x 75
= 117.75 m
Perimeter of shaded parts
= 94.2 + 70.65 + 117.75
= 1413 m
Answer(s): (a) 1350 m
2; (b) 1413 m