The figure is made up of a circle, a rectangle and 2 semicircles. YA, the diameter of the circle, is 125 m, YZ is 120 m and ZA is 35 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 YZ
= 120 ÷ 2
= 60 m
Area of Semicircle YZ
=
12 x 60 x 60 x 3.14
= 5652 m
2
Radius of ZA
= 35 ÷ 2
= 17.5 m
Area of Semicircle ZA
=
12 x 17.5 x 17.5 x 3.14
= 480.8125 m
2 Radius of YA
= 125 ÷ 2
= 62.5 m
Area of the semicircle YA = Radius YA
=
12 x 62.5 x 62.5 x 3.14
= 6132.8125 m
2 Total area of shaded parts
= 5652 + 480.8125 +
12 x 120 x 35 - 6132.8125
= 2100 m
2 (b)
Length of Semicircle YZ
=
12 x 3.14 x 120
= 188.4 m
Length of Semicircle ZA
=
12 x 3.14 x 35
= 54.95 m
Length of Semicircle YA
=
12 x 3.14 x 125
= 196.25 m
Perimeter of shaded parts
= 188.4 + 54.95 + 196.25
= 5652 m
Answer(s): (a) 2100 m
2; (b) 5652 m