The figure is made up of a right-angled triangle NPR and two semicircles with NP and PR as their diameters respectively. The two semicircles and the line NR meet at S as shown. NP = 18 cm. PR = 24 cm and NR = 30 cm. (Take π = 3.14)

1. Find the perimeter of the shaded region. Correct the answer to 2 decimal places.
2. Find the area of the shaded region.

(a)
Circumference of Semicircle NSP
= ¹₂ x 3.14 x 18
= 28.26 cm

Circumference of Semicircle RSP
= ¹₂ x 3.14 x 24
= 37.68 cm

Perimeter of shaded region
= Circumference of semicircles + NR
= 28.26 cm + 37.68 cm + 30 cm
= 95.94 cm

(b)
Area of Triangle NPR
= ¹₂ x 24 x 18
= 216 cm²

Area of Semicircle NSP
= ¹₂ x 3.14 x 9 x 9
= 127.17 cm²

Area of Semicircle RSP
= ¹₂ x 3.14 x 12 x 12
= 226.08 cm²

Area of the shaded region
= 127.17 + 226.08 - 216
= 137.25 cm²

Answer(s): (a) 95.94 cm; (b) 137.25 cm²