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 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line P) 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 + 4
= 24 m
Area of the big semicircle above the dotted line
= 3.14 x 24 x 24 x
12 = 904.32 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
= 904.32 - 628
= 276.32 m
2 Radius of the small semicircle below the dotted line
= 20 - 4
= 16 m
Area of the small semicircle below the dotted line
= 3.14 x 16 x 16 x 20
= 276.32 m
2 Shaded area below the dotted line
= 628 - 276.32
= 351.68 m
2 Total shaded area
= 276.32 + 351.68
= 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 + (4 x 2)
= 251.2 + 8
= 259.2 m
Answer(s): (a) 628 m
2; (b) 259.2 m