The figure is made up of a circle, a rectangle and 2 semicircles. LN, the diameter of the circle, is 50 m, LM is 48 m and MN is 14 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
= 48 ÷ 2
= 24 m
Area of Semicircle LM
=
12 x 24 x 24 x 3.14
= 904.32 m
2
Radius of MN
= 14 ÷ 2
= 7 m
Area of Semicircle MN
=
12 x 7 x 7 x 3.14
= 76.93 m
2 Radius of LN
= 50 ÷ 2
= 25 m
Area of the semicircle LN = Radius LN
=
12 x 25 x 25 x 3.14
= 981.25 m
2 Total area of shaded parts
= 904.32 + 76.93 +
12 x 48 x 14 - 981.25
= 336 m
2 (b)
Length of Semicircle LM
=
12 x 3.14 x 48
= 75.36 m
Length of Semicircle MN
=
12 x 3.14 x 14
= 21.98 m
Length of Semicircle LN
=
12 x 3.14 x 50
= 78.5 m
Perimeter of shaded parts
= 75.36 + 21.98 + 78.5
= 904.32 m
Answer(s): (a) 336 m
2; (b) 904.32 m