The figure is made up of a circle, a rectangle and 2 semicircles. GJ, the diameter of the circle, is 100 m, GH is 96 m and HJ is 28 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
= 96 ÷ 2
= 48 m
Area of Semicircle GH
=
12 x 48 x 48 x 3.14
= 3617.28 m
2
Radius of HJ
= 28 ÷ 2
= 14 m
Area of Semicircle HJ
=
12 x 14 x 14 x 3.14
= 307.72 m
2 Radius of GJ
= 100 ÷ 2
= 50 m
Area of the semicircle GJ = Radius GJ
=
12 x 50 x 50 x 3.14
= 3925 m
2 Total area of shaded parts
= 3617.28 + 307.72 +
12 x 96 x 28 - 3925
= 1344 m
2 (b)
Length of Semicircle GH
=
12 x 3.14 x 96
= 150.72 m
Length of Semicircle HJ
=
12 x 3.14 x 28
= 43.96 m
Length of Semicircle GJ
=
12 x 3.14 x 100
= 157 m
Perimeter of shaded parts
= 150.72 + 43.96 + 157
= 3617.28 m
Answer(s): (a) 1344 m
2; (b) 3617.28 m