The figure is made up of a circle, a rectangle and 2 semicircles. EG, the diameter of the circle, is 25 m, EF is 24 m and FG is 7 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 EF
= 24 ÷ 2
= 12 m
Area of Semicircle EF
=
12 x 12 x 12 x 3.14
= 226.08 m
2
Radius of FG
= 7 ÷ 2
= 3.5 m
Area of Semicircle FG
=
12 x 3.5 x 3.5 x 3.14
= 19.2325 m
2 Radius of EG
= 25 ÷ 2
= 12.5 m
Area of the semicircle EG = Radius EG
=
12 x 12.5 x 12.5 x 3.14
= 245.3125 m
2 Total area of shaded parts
= 226.08 + 19.2325 +
12 x 24 x 7 - 245.3125
= 84 m
2 (b)
Length of Semicircle EF
=
12 x 3.14 x 24
= 37.68 m
Length of Semicircle FG
=
12 x 3.14 x 7
= 10.99 m
Length of Semicircle EG
=
12 x 3.14 x 25
= 39.25 m
Perimeter of shaded parts
= 37.68 + 10.99 + 39.25
= 226.08 m
Answer(s): (a) 84 m
2; (b) 226.08 m