The figure is made up of a circle, a rectangle and 2 semicircles. MP, the diameter of the circle, is 45 cm, MN is 36 cm and NP is 27 cm.
- 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
= 36 ÷ 2
= 18 cm
Area of Semicircle MN
=
12 x 18 x 18 x 3.14
= 508.68 cm
2
Radius of NP
= 27 ÷ 2
= 13.5 cm
Area of Semicircle NP
=
12 x 13.5 x 13.5 x 3.14
= 286.1325 cm
2 Radius of MP
= 45 ÷ 2
= 22.5 cm
Area of the semicircle MP = Radius MP
=
12 x 22.5 x 22.5 x 3.14
= 794.8125 cm
2 Total area of shaded parts
= 508.68 + 286.1325 +
12 x 36 x 27 - 794.8125
= 486 cm
2 (b)
Length of Semicircle MN
=
12 x 3.14 x 36
= 56.52 cm
Length of Semicircle NP
=
12 x 3.14 x 27
= 42.39 cm
Length of Semicircle MP
=
12 x 3.14 x 45
= 70.65 cm
Perimeter of shaded parts
= 56.52 + 42.39 + 70.65
= 508.68 cm
Answer(s): (a) 486 cm
2; (b) 508.68 cm