The figure is made up of a right-angled triangle UVX and two semicircles with UV and VX as their diameters respectively. The two semicircles and the line UX meet at Y as shown. UV = 18 m. VX = 24 m and UX = 30 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 UYV
= ¹₂ x 3.14 x 18
= 28.26 m

Circumference of Semicircle XYV
= ¹₂ x 3.14 x 24
= 37.68 m

Perimeter of shaded region
= Circumference of semicircles + UX
= 28.26 m + 37.68 m + 30 m
= 95.94 m

(b)
Area of Triangle UVX
= ¹₂ x 24 x 18
= 216 m²

Area of Semicircle UYV
= ¹₂ x 3.14 x 9 x 9
= 127.17 m²

Area of Semicircle XYV
= ¹₂ x 3.14 x 12 x 12
= 226.08 m²

Area of the shaded region
= 127.17 + 226.08 - 216
= 137.25 m²

Answer(s): (a) 95.94 m; (b) 137.25 m²