The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 5 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line N) is 20 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
= 20 + 5
= 25 cm
Area of the big semicircle above the dotted line
= 3.14 x 25 x 25 x
12 = 981.25 cm
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 cm
2 Shaded area above the dotted line
= 981.25 - 628
= 353.25 cm
2 Radius of the small semicircle below the dotted line
= 20 - 5
= 15 cm
Area of the small semicircle below the dotted line
= 3.14 x 15 x 15 x 20
= 353.25 cm
2 Shaded area below the dotted line
= 628 - 353.25
= 274.75 cm
2 Total shaded area
= 353.25 + 274.75
= 628 cm
2 (b)
20 x 4 = 80 cm
Circumference of the curved lines
= 3.14 x 80
= 251.2 cm
Perimeter of the shaded area
= 251.2 + (5 x 2)
= 251.2 + 10
= 261.2 cm
Answer(s): (a) 628 cm
2; (b) 261.2 cm