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 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line H) is 12 cm.
- 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
= 12 + 9
= 21 cm
Area of the big semicircle above the dotted line
= 3.14 x 21 x 21 x
12 = 692.37 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 12 x 12 x
12 = 226.08 cm
2 Shaded area above the dotted line
= 692.37 - 226.08
= 466.29 cm
2 Radius of the small semicircle below the dotted line
= 12 - 9
= 3 cm
Area of the small semicircle below the dotted line
= 3.14 x 3 x 3 x 12
= 466.29 cm
2 Shaded area below the dotted line
= 226.08 - 466.29
= -240.21 cm
2 Total shaded area
= 466.29 + -240.21
= 226.08 cm
2 (b)
12 x 4 = 48 cm
Circumference of the curved lines
= 3.14 x 48
= 150.72 cm
Perimeter of the shaded area
= 150.72 + (9 x 2)
= 150.72 + 18
= 168.72 cm
Answer(s): (a) 226.08 cm
2; (b) 168.72 cm