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 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line M) is 38 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
= 38 + 7
= 45 cm
Area of the big semicircle above the dotted line
= 3.14 x 45 x 45 x
12 = 3179.25 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 38 x 38 x
12 = 2267.08 cm
2 Shaded area above the dotted line
= 3179.25 - 2267.08
= 912.17 cm
2 Radius of the small semicircle below the dotted line
= 38 - 7
= 31 cm
Area of the small semicircle below the dotted line
= 3.14 x 31 x 31 x 38
= 912.17 cm
2 Shaded area below the dotted line
= 2267.08 - 912.17
= 1354.91 cm
2 Total shaded area
= 912.17 + 1354.91
= 2267.08 cm
2 (b)
38 x 4 = 152 cm
Circumference of the curved lines
= 3.14 x 152
= 477.28 cm
Perimeter of the shaded area
= 477.28 + (7 x 2)
= 477.28 + 14
= 491.28 cm
Answer(s): (a) 2267.08 cm
2; (b) 491.28 cm