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 D) is 26 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
= 26 + 5
= 31 cm
Area of the big semicircle above the dotted line
= 3.14 x 31 x 31 x
12 = 1508.77 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 26 x 26 x
12 = 1061.32 cm
2 Shaded area above the dotted line
= 1508.77 - 1061.32
= 447.45 cm
2 Radius of the small semicircle below the dotted line
= 26 - 5
= 21 cm
Area of the small semicircle below the dotted line
= 3.14 x 21 x 21 x 26
= 447.45 cm
2 Shaded area below the dotted line
= 1061.32 - 447.45
= 613.87 cm
2 Total shaded area
= 447.45 + 613.87
= 1061.32 cm
2 (b)
26 x 4 = 104 cm
Circumference of the curved lines
= 3.14 x 104
= 326.56 cm
Perimeter of the shaded area
= 326.56 + (5 x 2)
= 326.56 + 10
= 336.56 cm
Answer(s): (a) 1061.32 cm
2; (b) 336.56 cm