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 C) is 12 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
= 12 + 5
= 17 m
Area of the big semicircle above the dotted line
= 3.14 x 17 x 17 x
12 = 453.73 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 12 x 12 x
12 = 226.08 m
2 Shaded area above the dotted line
= 453.73 - 226.08
= 227.65 m
2 Radius of the small semicircle below the dotted line
= 12 - 5
= 7 m
Area of the small semicircle below the dotted line
= 3.14 x 7 x 7 x 12
= 227.65 m
2 Shaded area below the dotted line
= 226.08 - 227.65
= -1.57 m
2 Total shaded area
= 227.65 + -1.57
= 226.08 m
2 (b)
12 x 4 = 48 m
Circumference of the curved lines
= 3.14 x 48
= 150.72 m
Perimeter of the shaded area
= 150.72 + (5 x 2)
= 150.72 + 10
= 160.72 m
Answer(s): (a) 226.08 m
2; (b) 160.72 m