The figure is made up of a circle, a rectangle and 2 semicircles. AC, the diameter of the circle, is 75 cm, AB is 60 cm and BC is 45 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 AB
= 60 ÷ 2
= 30 cm
Area of Semicircle AB
=
12 x 30 x 30 x 3.14
= 1413 cm
2
Radius of BC
= 45 ÷ 2
= 22.5 cm
Area of Semicircle BC
=
12 x 22.5 x 22.5 x 3.14
= 794.8125 cm
2 Radius of AC
= 75 ÷ 2
= 37.5 cm
Area of the semicircle AC = Radius AC
=
12 x 37.5 x 37.5 x 3.14
= 2207.8125 cm
2 Total area of shaded parts
= 1413 + 794.8125 +
12 x 60 x 45 - 2207.8125
= 1350 cm
2 (b)
Length of Semicircle AB
=
12 x 3.14 x 60
= 94.2 cm
Length of Semicircle BC
=
12 x 3.14 x 45
= 70.65 cm
Length of Semicircle AC
=
12 x 3.14 x 75
= 117.75 cm
Perimeter of shaded parts
= 94.2 + 70.65 + 117.75
= 1413 cm
Answer(s): (a) 1350 cm
2; (b) 1413 cm