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 X) is 36 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
= 36 + 5
= 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 36 x 36 x
12 = 2034.72 m
2 Shaded area above the dotted line
= 2639.17 - 2034.72
= 604.45 m
2 Radius of the small semicircle below the dotted line
= 36 - 5
= 31 m
Area of the small semicircle below the dotted line
= 3.14 x 31 x 31 x 36
= 604.45 m
2 Shaded area below the dotted line
= 2034.72 - 604.45
= 1430.27 m
2 Total shaded area
= 604.45 + 1430.27
= 2034.72 m
2 (b)
36 x 4 = 144 m
Circumference of the curved lines
= 3.14 x 144
= 452.16 m
Perimeter of the shaded area
= 452.16 + (5 x 2)
= 452.16 + 10
= 462.16 m
Answer(s): (a) 2034.72 m
2; (b) 462.16 m