The figure is made up of a circle, a rectangle and 2 semicircles. NQ, the diameter of the circle, is 30 cm, NP is 24 cm and PQ is 18 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 NP
= 24 ÷ 2
= 12 cm
Area of Semicircle NP
=
12 x 12 x 12 x 3.14
= 226.08 cm
2
Radius of PQ
= 18 ÷ 2
= 9 cm
Area of Semicircle PQ
=
12 x 9 x 9 x 3.14
= 127.17 cm
2 Radius of NQ
= 30 ÷ 2
= 15 cm
Area of the semicircle NQ = Radius NQ
=
12 x 15 x 15 x 3.14
= 353.25 cm
2 Total area of shaded parts
= 226.08 + 127.17 +
12 x 24 x 18 - 353.25
= 216 cm
2 (b)
Length of Semicircle NP
=
12 x 3.14 x 24
= 37.68 cm
Length of Semicircle PQ
=
12 x 3.14 x 18
= 28.26 cm
Length of Semicircle NQ
=
12 x 3.14 x 30
= 47.1 cm
Perimeter of shaded parts
= 37.68 + 28.26 + 47.1
= 226.08 cm
Answer(s): (a) 216 cm
2; (b) 226.08 cm