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