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 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Q) is 12 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
= 12 + 7
= 19 m
Area of the big semicircle above the dotted line
= 3.14 x 19 x 19 x
12 = 566.77 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 12 x 12 x
12 = 226.08 m
2 Shaded area above the dotted line
= 566.77 - 226.08
= 340.69 m
2 Radius of the small semicircle below the dotted line
= 12 - 7
= 5 m
Area of the small semicircle below the dotted line
= 3.14 x 5 x 5 x 12
= 340.69 m
2 Shaded area below the dotted line
= 226.08 - 340.69
= -114.61 m
2 Total shaded area
= 340.69 + -114.61
= 226.08 m
2 (b)
12 x 4 = 48 m
Circumference of the curved lines
= 3.14 x 48
= 150.72 m
Perimeter of the shaded area
= 150.72 + (7 x 2)
= 150.72 + 14
= 164.72 m
Answer(s): (a) 226.08 m
2; (b) 164.72 m