The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 6 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line B) is 30 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
= 30 + 6
= 36 m
Area of the big semicircle above the dotted line
= 3.14 x 36 x 36 x
12 = 2034.72 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 30 x 30 x
12 = 1413 m
2 Shaded area above the dotted line
= 2034.72 - 1413
= 621.72 m
2 Radius of the small semicircle below the dotted line
= 30 - 6
= 24 m
Area of the small semicircle below the dotted line
= 3.14 x 24 x 24 x 30
= 621.72 m
2 Shaded area below the dotted line
= 1413 - 621.72
= 791.28 m
2 Total shaded area
= 621.72 + 791.28
= 1413 m
2 (b)
30 x 4 = 120 m
Circumference of the curved lines
= 3.14 x 120
= 376.8 m
Perimeter of the shaded area
= 376.8 + (6 x 2)
= 376.8 + 12
= 388.8 m
Answer(s): (a) 1413 m
2; (b) 388.8 m