The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 6 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line X) is 10 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
= 10 + 6
= 16 cm
Area of the big semicircle above the dotted line
= 3.14 x 16 x 16 x
12 = 401.92 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 10 x 10 x
12 = 157 cm
2 Shaded area above the dotted line
= 401.92 - 157
= 244.92 cm
2 Radius of the small semicircle below the dotted line
= 10 - 6
= 4 cm
Area of the small semicircle below the dotted line
= 3.14 x 4 x 4 x 10
= 244.92 cm
2 Shaded area below the dotted line
= 157 - 244.92
= -87.92 cm
2 Total shaded area
= 244.92 + -87.92
= 157 cm
2 (b)
10 x 4 = 40 cm
Circumference of the curved lines
= 3.14 x 40
= 125.6 cm
Perimeter of the shaded area
= 125.6 + (6 x 2)
= 125.6 + 12
= 137.6 cm
Answer(s): (a) 157 cm
2; (b) 137.6 cm