The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 3 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line E) is 38 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
= 38 + 3
= 41 m
Area of the big semicircle above the dotted line
= 3.14 x 41 x 41 x
12 = 2639.17 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 38 x 38 x
12 = 2267.08 m
2 Shaded area above the dotted line
= 2639.17 - 2267.08
= 372.09 m
2 Radius of the small semicircle below the dotted line
= 38 - 3
= 35 m
Area of the small semicircle below the dotted line
= 3.14 x 35 x 35 x 38
= 372.09 m
2 Shaded area below the dotted line
= 2267.08 - 372.09
= 1894.99 m
2 Total shaded area
= 372.09 + 1894.99
= 2267.08 m
2 (b)
38 x 4 = 152 m
Circumference of the curved lines
= 3.14 x 152
= 477.28 m
Perimeter of the shaded area
= 477.28 + (3 x 2)
= 477.28 + 6
= 483.28 m
Answer(s): (a) 2267.08 m
2; (b) 483.28 m