The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 8 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line R) 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 + 8
= 28 m
Area of the big semicircle above the dotted line
= 3.14 x 28 x 28 x
12 = 1230.88 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
= 1230.88 - 628
= 602.88 m
2 Radius of the small semicircle below the dotted line
= 20 - 8
= 12 m
Area of the small semicircle below the dotted line
= 3.14 x 12 x 12 x 20
= 602.88 m
2 Shaded area below the dotted line
= 628 - 602.88
= 25.12 m
2 Total shaded area
= 602.88 + 25.12
= 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 + (8 x 2)
= 251.2 + 16
= 267.2 m
Answer(s): (a) 628 m
2; (b) 267.2 m