The figure is made up of a circle, a rectangle and 2 semicircles. MP, the diameter of the circle, is 10 m, MN is 8 m and NP is 6 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 MN
= 8 ÷ 2
= 4 m
Area of Semicircle MN
=
12 x 4 x 4 x 3.14
= 25.12 m
2
Radius of NP
= 6 ÷ 2
= 3 m
Area of Semicircle NP
=
12 x 3 x 3 x 3.14
= 14.13 m
2 Radius of MP
= 10 ÷ 2
= 5 m
Area of the semicircle MP = Radius MP
=
12 x 5 x 5 x 3.14
= 39.25 m
2 Total area of shaded parts
= 25.12 + 14.13 +
12 x 8 x 6 - 39.25
= 24 m
2 (b)
Length of Semicircle MN
=
12 x 3.14 x 8
= 12.56 m
Length of Semicircle NP
=
12 x 3.14 x 6
= 9.42 m
Length of Semicircle MP
=
12 x 3.14 x 10
= 15.7 m
Perimeter of shaded parts
= 12.56 + 9.42 + 15.7
= 25.12 m
Answer(s): (a) 24 m
2; (b) 25.12 m