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 Q) is 20 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
= 20 + 9
= 29 m
Area of the big semicircle above the dotted line
= 3.14 x 29 x 29 x
12 = 1320.37 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 20 x 20 x
12 = 628 m
2 Shaded area above the dotted line
= 1320.37 - 628
= 692.37 m
2 Radius of the small semicircle below the dotted line
= 20 - 9
= 11 m
Area of the small semicircle below the dotted line
= 3.14 x 11 x 11 x 20
= 692.37 m
2 Shaded area below the dotted line
= 628 - 692.37
= -64.37 m
2 Total shaded area
= 692.37 + -64.37
= 628 m
2 (b)
20 x 4 = 80 m
Circumference of the curved lines
= 3.14 x 80
= 251.2 m
Perimeter of the shaded area
= 251.2 + (9 x 2)
= 251.2 + 18
= 269.2 m
Answer(s): (a) 628 m
2; (b) 269.2 m