The figure is made up of a circle, a rectangle and 2 semicircles. DF, the diameter of the circle, is 15 cm, DE is 12 cm and EF is 9 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 DE
= 12 ÷ 2
= 6 cm
Area of Semicircle DE
=
12 x 6 x 6 x 3.14
= 56.52 cm
2
Radius of EF
= 9 ÷ 2
= 4.5 cm
Area of Semicircle EF
=
12 x 4.5 x 4.5 x 3.14
= 31.7925 cm
2 Radius of DF
= 15 ÷ 2
= 7.5 cm
Area of the semicircle DF = Radius DF
=
12 x 7.5 x 7.5 x 3.14
= 88.3125 cm
2 Total area of shaded parts
= 56.52 + 31.7925 +
12 x 12 x 9 - 88.3125
= 54 cm
2 (b)
Length of Semicircle DE
=
12 x 3.14 x 12
= 18.84 cm
Length of Semicircle EF
=
12 x 3.14 x 9
= 14.13 cm
Length of Semicircle DF
=
12 x 3.14 x 15
= 23.55 cm
Perimeter of shaded parts
= 18.84 + 14.13 + 23.55
= 56.52 cm
Answer(s): (a) 54 cm
2; (b) 56.52 cm