The figure is made up of a circle, a rectangle and 2 semicircles. TV, the diameter of the circle, is 5 cm, TU is 4 cm and UV is 3 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 TU
= 4 ÷ 2
= 2 cm
Area of Semicircle TU
=
12 x 2 x 2 x 3.14
= 6.28 cm
2
Radius of UV
= 3 ÷ 2
= 1.5 cm
Area of Semicircle UV
=
12 x 1.5 x 1.5 x 3.14
= 3.5325 cm
2 Radius of TV
= 5 ÷ 2
= 2.5 cm
Area of the semicircle TV = Radius TV
=
12 x 2.5 x 2.5 x 3.14
= 9.8125 cm
2 Total area of shaded parts
= 6.28 + 3.5325 +
12 x 4 x 3 - 9.8125
= 6 cm
2 (b)
Length of Semicircle TU
=
12 x 3.14 x 4
= 6.28 cm
Length of Semicircle UV
=
12 x 3.14 x 3
= 4.71 cm
Length of Semicircle TV
=
12 x 3.14 x 5
= 7.85 cm
Perimeter of shaded parts
= 6.28 + 4.71 + 7.85
= 6.28 cm
Answer(s): (a) 6 cm
2; (b) 6.28 cm