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 S) is 36 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
= 36 + 8
= 44 m
Area of the big semicircle above the dotted line
= 3.14 x 44 x 44 x
12 = 3039.52 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 36 x 36 x
12 = 2034.72 m
2 Shaded area above the dotted line
= 3039.52 - 2034.72
= 1004.8 m
2 Radius of the small semicircle below the dotted line
= 36 - 8
= 28 m
Area of the small semicircle below the dotted line
= 3.14 x 28 x 28 x 36
= 1004.8 m
2 Shaded area below the dotted line
= 2034.72 - 1004.8
= 1029.92 m
2 Total shaded area
= 1004.8 + 1029.92
= 2034.72 m
2 (b)
36 x 4 = 144 m
Circumference of the curved lines
= 3.14 x 144
= 452.16 m
Perimeter of the shaded area
= 452.16 + (8 x 2)
= 452.16 + 16
= 468.16 m
Answer(s): (a) 2034.72 m
2; (b) 468.16 m