The figure is made up of a right-angled triangle PRS and two semicircles with PR and RS as their diameters respectively. The two semicircles and the line PS meet at T as shown. PR = 10 cm. RS = 24 cm and PS = 26 cm. (Take π = 3.14)
- Find the perimeter of the shaded region. Correct the answer to 2 decimal places.
- Find the area of the shaded region.
(a)
Circumference of Semicircle PTR
=
12 x 3.14 x 10
= 15.7 cm
Circumference of Semicircle STR
=
12 x 3.14 x 24
= 37.68 cm
Perimeter of shaded region
= Circumference of semicircles + PS
= 15.7 cm + 37.68 cm + 26 cm
= 79.38 cm
(b)
Area of Triangle PRS
=
12 x 24 x 10
= 120 cm
2 Area of Semicircle PTR
=
12 x 3.14 x 5 x 5
= 39.25 cm
2 Area of Semicircle STR
=
12 x 3.14 x 12 x 12
= 226.08 cm
2 Area of the shaded region
= 39.25 + 226.08 - 120
= 145.33 cm
2 Answer(s): (a) 79.38 cm; (b) 145.33 cm
2