The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 4 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line E) 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 + 4
= 28 cm
Area of the big semicircle above the dotted line
= 3.14 x 28 x 28 x
12 = 1230.88 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
= 1230.88 - 904.32
= 326.56 cm
2 Radius of the small semicircle below the dotted line
= 24 - 4
= 20 cm
Area of the small semicircle below the dotted line
= 3.14 x 20 x 20 x 24
= 326.56 cm
2 Shaded area below the dotted line
= 904.32 - 326.56
= 577.76 cm
2 Total shaded area
= 326.56 + 577.76
= 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 + (4 x 2)
= 301.44 + 8
= 309.44 cm
Answer(s): (a) 904.32 cm
2; (b) 309.44 cm