The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 8 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Y) is 14 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
= 14 + 8
= 22 m
Area of the big semicircle above the dotted line
= 3.14 x 22 x 22 x
12 = 759.88 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 14 x 14 x
12 = 307.72 m
2 Shaded area above the dotted line
= 759.88 - 307.72
= 452.16 m
2 Radius of the small semicircle below the dotted line
= 14 - 8
= 6 m
Area of the small semicircle below the dotted line
= 3.14 x 6 x 6 x 14
= 452.16 m
2 Shaded area below the dotted line
= 307.72 - 452.16
= -144.44 m
2 Total shaded area
= 452.16 + -144.44
= 307.72 m
2 (b)
14 x 4 = 56 m
Circumference of the curved lines
= 3.14 x 56
= 175.84 m
Perimeter of the shaded area
= 175.84 + (8 x 2)
= 175.84 + 16
= 191.84 m
Answer(s): (a) 307.72 m
2; (b) 191.84 m