The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 4 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line L) is 14 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
= 14 + 4
= 18 m
Area of the big semicircle above the dotted line
= 3.14 x 18 x 18 x
12 = 508.68 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 14 x 14 x
12 = 307.72 m
2 Shaded area above the dotted line
= 508.68 - 307.72
= 200.96 m
2 Radius of the small semicircle below the dotted line
= 14 - 4
= 10 m
Area of the small semicircle below the dotted line
= 3.14 x 10 x 10 x 14
= 200.96 m
2 Shaded area below the dotted line
= 307.72 - 200.96
= 106.76 m
2 Total shaded area
= 200.96 + 106.76
= 307.72 m
2 (b)
14 x 4 = 56 m
Circumference of the curved lines
= 3.14 x 56
= 175.84 m
Perimeter of the shaded area
= 175.84 + (4 x 2)
= 175.84 + 8
= 183.84 m
Answer(s): (a) 307.72 m
2; (b) 183.84 m