The figure is made up of a circle, a rectangle and 2 semicircles. RT, the diameter of the circle, is 75 cm, RS is 72 cm and ST is 21 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 RS
= 72 ÷ 2
= 36 cm
Area of Semicircle RS
=
12 x 36 x 36 x 3.14
= 2034.72 cm
2
Radius of ST
= 21 ÷ 2
= 10.5 cm
Area of Semicircle ST
=
12 x 10.5 x 10.5 x 3.14
= 173.0925 cm
2 Radius of RT
= 75 ÷ 2
= 37.5 cm
Area of the semicircle RT = Radius RT
=
12 x 37.5 x 37.5 x 3.14
= 2207.8125 cm
2 Total area of shaded parts
= 2034.72 + 173.0925 +
12 x 72 x 21 - 2207.8125
= 756 cm
2 (b)
Length of Semicircle RS
=
12 x 3.14 x 72
= 113.04 cm
Length of Semicircle ST
=
12 x 3.14 x 21
= 32.97 cm
Length of Semicircle RT
=
12 x 3.14 x 75
= 117.75 cm
Perimeter of shaded parts
= 113.04 + 32.97 + 117.75
= 2034.72 cm
Answer(s): (a) 756 cm
2; (b) 2034.72 cm