The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 9 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line D) is 24 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
= 24 + 9
= 33 m
Area of the big semicircle above the dotted line
= 3.14 x 33 x 33 x
12 = 1709.73 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 24 x 24 x
12 = 904.32 m
2 Shaded area above the dotted line
= 1709.73 - 904.32
= 805.41 m
2 Radius of the small semicircle below the dotted line
= 24 - 9
= 15 m
Area of the small semicircle below the dotted line
= 3.14 x 15 x 15 x 24
= 805.41 m
2 Shaded area below the dotted line
= 904.32 - 805.41
= 98.91 m
2 Total shaded area
= 805.41 + 98.91
= 904.32 m
2 (b)
24 x 4 = 96 m
Circumference of the curved lines
= 3.14 x 96
= 301.44 m
Perimeter of the shaded area
= 301.44 + (9 x 2)
= 301.44 + 18
= 319.44 m
Answer(s): (a) 904.32 m
2; (b) 319.44 m