The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 7 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Q) is 14 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
= 14 + 7
= 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 14 x 14 x
12 = 307.72 cm
2 Shaded area above the dotted line
= 692.37 - 307.72
= 384.65 cm
2 Radius of the small semicircle below the dotted line
= 14 - 7
= 7 cm
Area of the small semicircle below the dotted line
= 3.14 x 7 x 7 x 14
= 384.65 cm
2 Shaded area below the dotted line
= 307.72 - 384.65
= -76.93 cm
2 Total shaded area
= 384.65 + -76.93
= 307.72 cm
2 (b)
14 x 4 = 56 cm
Circumference of the curved lines
= 3.14 x 56
= 175.84 cm
Perimeter of the shaded area
= 175.84 + (7 x 2)
= 175.84 + 14
= 189.84 cm
Answer(s): (a) 307.72 cm
2; (b) 189.84 cm