The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 8 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line J) is 12 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
= 12 + 8
= 20 cm
Area of the big semicircle above the dotted line
= 3.14 x 20 x 20 x
12 = 628 cm
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 cm
2 Shaded area above the dotted line
= 628 - 226.08
= 401.92 cm
2 Radius of the small semicircle below the dotted line
= 12 - 8
= 4 cm
Area of the small semicircle below the dotted line
= 3.14 x 4 x 4 x 12
= 401.92 cm
2 Shaded area below the dotted line
= 226.08 - 401.92
= -175.84 cm
2 Total shaded area
= 401.92 + -175.84
= 226.08 cm
2 (b)
12 x 4 = 48 cm
Circumference of the curved lines
= 3.14 x 48
= 150.72 cm
Perimeter of the shaded area
= 150.72 + (8 x 2)
= 150.72 + 16
= 166.72 cm
Answer(s): (a) 226.08 cm
2; (b) 166.72 cm