The figure is made up of a circle, a rectangle and 2 semicircles. LN, the diameter of the circle, is 75 m, LM is 72 m and MN is 21 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 LM
= 72 ÷ 2
= 36 m
Area of Semicircle LM
=
12 x 36 x 36 x 3.14
= 2034.72 m
2
Radius of MN
= 21 ÷ 2
= 10.5 m
Area of Semicircle MN
=
12 x 10.5 x 10.5 x 3.14
= 173.0925 m
2 Radius of LN
= 75 ÷ 2
= 37.5 m
Area of the semicircle LN = Radius LN
=
12 x 37.5 x 37.5 x 3.14
= 2207.8125 m
2 Total area of shaded parts
= 2034.72 + 173.0925 +
12 x 72 x 21 - 2207.8125
= 756 m
2 (b)
Length of Semicircle LM
=
12 x 3.14 x 72
= 113.04 m
Length of Semicircle MN
=
12 x 3.14 x 21
= 32.97 m
Length of Semicircle LN
=
12 x 3.14 x 75
= 117.75 m
Perimeter of shaded parts
= 113.04 + 32.97 + 117.75
= 2034.72 m
Answer(s): (a) 756 m
2; (b) 2034.72 m