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 S) is 24 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
= 24 + 7
= 31 cm
Area of the big semicircle above the dotted line
= 3.14 x 31 x 31 x
12 = 1508.77 cm
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 cm
2 Shaded area above the dotted line
= 1508.77 - 904.32
= 604.45 cm
2 Radius of the small semicircle below the dotted line
= 24 - 7
= 17 cm
Area of the small semicircle below the dotted line
= 3.14 x 17 x 17 x 24
= 604.45 cm
2 Shaded area below the dotted line
= 904.32 - 604.45
= 299.87 cm
2 Total shaded area
= 604.45 + 299.87
= 904.32 cm
2 (b)
24 x 4 = 96 cm
Circumference of the curved lines
= 3.14 x 96
= 301.44 cm
Perimeter of the shaded area
= 301.44 + (7 x 2)
= 301.44 + 14
= 315.44 cm
Answer(s): (a) 904.32 cm
2; (b) 315.44 cm