The figure is made up of a circle, a rectangle and 2 semicircles. ZB, the diameter of the circle, is 25 cm, ZA is 20 cm and AB is 15 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 ZA
= 20 ÷ 2
= 10 cm
Area of Semicircle ZA
=
12 x 10 x 10 x 3.14
= 157 cm
2
Radius of AB
= 15 ÷ 2
= 7.5 cm
Area of Semicircle AB
=
12 x 7.5 x 7.5 x 3.14
= 88.3125 cm
2 Radius of ZB
= 25 ÷ 2
= 12.5 cm
Area of the semicircle ZB = Radius ZB
=
12 x 12.5 x 12.5 x 3.14
= 245.3125 cm
2 Total area of shaded parts
= 157 + 88.3125 +
12 x 20 x 15 - 245.3125
= 150 cm
2 (b)
Length of Semicircle ZA
=
12 x 3.14 x 20
= 31.4 cm
Length of Semicircle AB
=
12 x 3.14 x 15
= 23.55 cm
Length of Semicircle ZB
=
12 x 3.14 x 25
= 39.25 cm
Perimeter of shaded parts
= 31.4 + 23.55 + 39.25
= 157 cm
Answer(s): (a) 150 cm
2; (b) 157 cm