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 U) is 22 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
= 22 + 9
= 31 m
Area of the big semicircle above the dotted line
= 3.14 x 31 x 31 x
12 = 1508.77 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 22 x 22 x
12 = 759.88 m
2 Shaded area above the dotted line
= 1508.77 - 759.88
= 748.89 m
2 Radius of the small semicircle below the dotted line
= 22 - 9
= 13 m
Area of the small semicircle below the dotted line
= 3.14 x 13 x 13 x 22
= 748.89 m
2 Shaded area below the dotted line
= 759.88 - 748.89
= 10.99 m
2 Total shaded area
= 748.89 + 10.99
= 759.88 m
2 (b)
22 x 4 = 88 m
Circumference of the curved lines
= 3.14 x 88
= 276.32 m
Perimeter of the shaded area
= 276.32 + (9 x 2)
= 276.32 + 18
= 294.32 m
Answer(s): (a) 759.88 m
2; (b) 294.32 m
