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 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line M) 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 + 7
= 33 m
Area of the big semicircle above the dotted line
= 3.14 x 33 x 33 x
12 = 1709.73 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
= 1709.73 - 1061.32
= 648.41 m
2 Radius of the small semicircle below the dotted line
= 26 - 7
= 19 m
Area of the small semicircle below the dotted line
= 3.14 x 19 x 19 x 26
= 648.41 m
2 Shaded area below the dotted line
= 1061.32 - 648.41
= 412.91 m
2 Total shaded area
= 648.41 + 412.91
= 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 + (7 x 2)
= 326.56 + 14
= 340.56 m
Answer(s): (a) 1061.32 m
2; (b) 340.56 m