The figure is made up of a right-angled triangle VXY and two semicircles with VX and XY as their diameters respectively. The two semicircles and the line VY meet at Z as shown. VX = 6 m. XY = 8 m and VY = 10 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 VZX
= ¹₂ x 3.14 x 6
= 9.42 m

Circumference of Semicircle YZX
= ¹₂ x 3.14 x 8
= 12.56 m

Perimeter of shaded region
= Circumference of semicircles + VY
= 9.42 m + 12.56 m + 10 m
= 31.98 m

(b)
Area of Triangle VXY
= ¹₂ x 8 x 6
= 24 m²

Area of Semicircle VZX
= ¹₂ x 3.14 x 3 x 3
= 14.13 m²

Area of Semicircle YZX
= ¹₂ x 3.14 x 4 x 4
= 25.12 m²

Area of the shaded region
= 14.13 + 25.12 - 24
= 15.25 m²

Answer(s): (a) 31.98 m; (b) 15.25 m²