The figure is made up of a circle, a rectangle and 2 semicircles. GJ, the diameter of the circle, is 15 m, GH is 12 m and HJ is 9 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 GH
= 12 ÷ 2
= 6 m
Area of Semicircle GH
=
12 x 6 x 6 x 3.14
= 56.52 m
2
Radius of HJ
= 9 ÷ 2
= 4.5 m
Area of Semicircle HJ
=
12 x 4.5 x 4.5 x 3.14
= 31.7925 m
2 Radius of GJ
= 15 ÷ 2
= 7.5 m
Area of the semicircle GJ = Radius GJ
=
12 x 7.5 x 7.5 x 3.14
= 88.3125 m
2 Total area of shaded parts
= 56.52 + 31.7925 +
12 x 12 x 9 - 88.3125
= 54 m
2 (b)
Length of Semicircle GH
=
12 x 3.14 x 12
= 18.84 m
Length of Semicircle HJ
=
12 x 3.14 x 9
= 14.13 m
Length of Semicircle GJ
=
12 x 3.14 x 15
= 23.55 m
Perimeter of shaded parts
= 18.84 + 14.13 + 23.55
= 56.52 m
Answer(s): (a) 54 m
2; (b) 56.52 m