The figure is made up of a circle, a rectangle and 2 semicircles. PR, the diameter of the circle, is 100 cm, PQ is 96 cm and QR is 28 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 PQ
= 96 ÷ 2
= 48 cm
Area of Semicircle PQ
=
12 x 48 x 48 x 3.14
= 3617.28 cm
2
Radius of QR
= 28 ÷ 2
= 14 cm
Area of Semicircle QR
=
12 x 14 x 14 x 3.14
= 307.72 cm
2 Radius of PR
= 100 ÷ 2
= 50 cm
Area of the semicircle PR = Radius PR
=
12 x 50 x 50 x 3.14
= 3925 cm
2 Total area of shaded parts
= 3617.28 + 307.72 +
12 x 96 x 28 - 3925
= 1344 cm
2 (b)
Length of Semicircle PQ
=
12 x 3.14 x 96
= 150.72 cm
Length of Semicircle QR
=
12 x 3.14 x 28
= 43.96 cm
Length of Semicircle PR
=
12 x 3.14 x 100
= 157 cm
Perimeter of shaded parts
= 150.72 + 43.96 + 157
= 3617.28 cm
Answer(s): (a) 1344 cm
2; (b) 3617.28 cm