The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 8 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Z) is 28 m.
- Find the area of the shaded part.
- Find the perimeter of the dotted line. (Take π = 3.14)
(a)
Radius of the big semicircle above the dotted line
= 28 + 8
= 36 m
Area of the big semicircle above the dotted line
= 3.14 x 36 x 36 x
12 = 2034.72 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 28 x 28 x
12 = 1230.88 m
2 Shaded area above the dotted line
= 2034.72 - 1230.88
= 803.84 m
2 Radius of the small semicircle below the dotted line
= 28 - 8
= 20 m
Area of the small semicircle below the dotted line
= 3.14 x 20 x 20 x 28
= 803.84 m
2 Shaded area below the dotted line
= 1230.88 - 803.84
= 427.04 m
2 Total shaded area
= 803.84 + 427.04
= 1230.88 m
2 (b)
28 x 4 = 112 m
Circumference of the curved lines
= 3.14 x 112
= 351.68 m
Perimeter of the shaded area
= 351.68 + (8 x 2)
= 351.68 + 16
= 367.68 m
Answer(s): (a) 1230.88 m
2; (b) 367.68 m