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 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line S) is 26 m.
- 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 + 6
= 32 m
Area of the big semicircle above the dotted line
= 3.14 x 32 x 32 x
12 = 1607.68 m
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 m
2 Shaded area above the dotted line
= 1607.68 - 1061.32
= 546.36 m
2 Radius of the small semicircle below the dotted line
= 26 - 6
= 20 m
Area of the small semicircle below the dotted line
= 3.14 x 20 x 20 x 26
= 546.36 m
2 Shaded area below the dotted line
= 1061.32 - 546.36
= 514.96 m
2 Total shaded area
= 546.36 + 514.96
= 1061.32 m
2 (b)
26 x 4 = 104 m
Circumference of the curved lines
= 3.14 x 104
= 326.56 m
Perimeter of the shaded area
= 326.56 + (6 x 2)
= 326.56 + 12
= 338.56 m
Answer(s): (a) 1061.32 m
2; (b) 338.56 m