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