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 H) is 40 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
= 40 + 3
= 43 m
Area of the big semicircle above the dotted line
= 3.14 x 43 x 43 x
12 = 2902.93 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 40 x 40 x
12 = 2512 m
2 Shaded area above the dotted line
= 2902.93 - 2512
= 390.93 m
2 Radius of the small semicircle below the dotted line
= 40 - 3
= 37 m
Area of the small semicircle below the dotted line
= 3.14 x 37 x 37 x 40
= 390.93 m
2 Shaded area below the dotted line
= 2512 - 390.93
= 2121.07 m
2 Total shaded area
= 390.93 + 2121.07
= 2512 m
2 (b)
40 x 4 = 160 m
Circumference of the curved lines
= 3.14 x 160
= 502.4 m
Perimeter of the shaded area
= 502.4 + (3 x 2)
= 502.4 + 6
= 508.4 m
Answer(s): (a) 2512 m
2; (b) 508.4 m