The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 5 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line R) is 18 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
= 18 + 5
= 23 m
Area of the big semicircle above the dotted line
= 3.14 x 23 x 23 x
12 = 830.53 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 18 x 18 x
12 = 508.68 m
2 Shaded area above the dotted line
= 830.53 - 508.68
= 321.85 m
2 Radius of the small semicircle below the dotted line
= 18 - 5
= 13 m
Area of the small semicircle below the dotted line
= 3.14 x 13 x 13 x 18
= 321.85 m
2 Shaded area below the dotted line
= 508.68 - 321.85
= 186.83 m
2 Total shaded area
= 321.85 + 186.83
= 508.68 m
2 (b)
18 x 4 = 72 m
Circumference of the curved lines
= 3.14 x 72
= 226.08 m
Perimeter of the shaded area
= 226.08 + (5 x 2)
= 226.08 + 10
= 236.08 m
Answer(s): (a) 508.68 m
2; (b) 236.08 m