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 = 12 m. PR = 16 m and NR = 20 m. (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 12
= 18.84 m

Circumference of Semicircle RSP
= ¹₂ x 3.14 x 16
= 25.12 m

Perimeter of shaded region
= Circumference of semicircles + NR
= 18.84 m + 25.12 m + 20 m
= 63.96 m

(b)
Area of Triangle NPR
= ¹₂ x 16 x 12
= 96 m²

Area of Semicircle NSP
= ¹₂ x 3.14 x 6 x 6
= 56.52 m²

Area of Semicircle RSP
= ¹₂ x 3.14 x 8 x 8
= 100.48 m²

Area of the shaded region
= 56.52 + 100.48 - 96
= 61 m²

Answer(s): (a) 63.96 m; (b) 61 m²