The figure is made up of a circle, a rectangle and 2 semicircles. FH, the diameter of the circle, is 5 m, FG is 4 m and GH is 3 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 FG
= 4 ÷ 2
= 2 m
Area of Semicircle FG
=
12 x 2 x 2 x 3.14
= 6.28 m
2
Radius of GH
= 3 ÷ 2
= 1.5 m
Area of Semicircle GH
=
12 x 1.5 x 1.5 x 3.14
= 3.5325 m
2 Radius of FH
= 5 ÷ 2
= 2.5 m
Area of the semicircle FH = Radius FH
=
12 x 2.5 x 2.5 x 3.14
= 9.8125 m
2 Total area of shaded parts
= 6.28 + 3.5325 +
12 x 4 x 3 - 9.8125
= 6 m
2 (b)
Length of Semicircle FG
=
12 x 3.14 x 4
= 6.28 m
Length of Semicircle GH
=
12 x 3.14 x 3
= 4.71 m
Length of Semicircle FH
=
12 x 3.14 x 5
= 7.85 m
Perimeter of shaded parts
= 6.28 + 4.71 + 7.85
= 6.28 m
Answer(s): (a) 6 m
2; (b) 6.28 m