The figure is made up of a circle, a rectangle and 2 semicircles. RT, the diameter of the circle, is 50 cm, RS is 48 cm and ST is 14 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
= 48 ÷ 2
= 24 cm
Area of Semicircle RS
=
12 x 24 x 24 x 3.14
= 904.32 cm
2
Radius of ST
= 14 ÷ 2
= 7 cm
Area of Semicircle ST
=
12 x 7 x 7 x 3.14
= 76.93 cm
2 Radius of RT
= 50 ÷ 2
= 25 cm
Area of the semicircle RT = Radius RT
=
12 x 25 x 25 x 3.14
= 981.25 cm
2 Total area of shaded parts
= 904.32 + 76.93 +
12 x 48 x 14 - 981.25
= 336 cm
2 (b)
Length of Semicircle RS
=
12 x 3.14 x 48
= 75.36 cm
Length of Semicircle ST
=
12 x 3.14 x 14
= 21.98 cm
Length of Semicircle RT
=
12 x 3.14 x 50
= 78.5 cm
Perimeter of shaded parts
= 75.36 + 21.98 + 78.5
= 904.32 cm
Answer(s): (a) 336 cm
2; (b) 904.32 cm