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 = 10 m. XY = 24 m and VY = 26 m. (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 VZX
=
12 x 3.14 x 10
= 15.7 m
Circumference of Semicircle YZX
=
12 x 3.14 x 24
= 37.68 m
Perimeter of shaded region
= Circumference of semicircles + VY
= 15.7 m + 37.68 m + 26 m
= 79.38 m
(b)
Area of Triangle VXY
=
12 x 24 x 10
= 120 m
2 Area of Semicircle VZX
=
12 x 3.14 x 5 x 5
= 39.25 m
2 Area of Semicircle YZX
=
12 x 3.14 x 12 x 12
= 226.08 m
2 Area of the shaded region
= 39.25 + 226.08 - 120
= 145.33 m
2 Answer(s): (a) 79.38 m; (b) 145.33 m
2