The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 7 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line M) is 10 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
= 10 + 7
= 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 10 x 10 x
12 = 157 m
2 Shaded area above the dotted line
= 453.73 - 157
= 296.73 m
2 Radius of the small semicircle below the dotted line
= 10 - 7
= 3 m
Area of the small semicircle below the dotted line
= 3.14 x 3 x 3 x 10
= 296.73 m
2 Shaded area below the dotted line
= 157 - 296.73
= -139.73 m
2 Total shaded area
= 296.73 + -139.73
= 157 m
2 (b)
10 x 4 = 40 m
Circumference of the curved lines
= 3.14 x 40
= 125.6 m
Perimeter of the shaded area
= 125.6 + (7 x 2)
= 125.6 + 14
= 139.6 m
Answer(s): (a) 157 m
2; (b) 139.6 m