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 S) is 16 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
= 16 + 7
= 23 m
Area of the big semicircle above the dotted line
= 3.14 x 23 x 23 x
12 = 830.53 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 16 x 16 x
12 = 401.92 m
2 Shaded area above the dotted line
= 830.53 - 401.92
= 428.61 m
2 Radius of the small semicircle below the dotted line
= 16 - 7
= 9 m
Area of the small semicircle below the dotted line
= 3.14 x 9 x 9 x 16
= 428.61 m
2 Shaded area below the dotted line
= 401.92 - 428.61
= -26.69 m
2 Total shaded area
= 428.61 + -26.69
= 401.92 m
2 (b)
16 x 4 = 64 m
Circumference of the curved lines
= 3.14 x 64
= 200.96 m
Perimeter of the shaded area
= 200.96 + (7 x 2)
= 200.96 + 14
= 214.96 m
Answer(s): (a) 401.92 m
2; (b) 214.96 m