The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 3 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Y) 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 + 3
= 29 cm
Area of the big semicircle above the dotted line
= 3.14 x 29 x 29 x
12 = 1320.37 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
= 1320.37 - 1061.32
= 259.05 cm
2 Radius of the small semicircle below the dotted line
= 26 - 3
= 23 cm
Area of the small semicircle below the dotted line
= 3.14 x 23 x 23 x 26
= 259.05 cm
2 Shaded area below the dotted line
= 1061.32 - 259.05
= 802.27 cm
2 Total shaded area
= 259.05 + 802.27
= 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 + (3 x 2)
= 326.56 + 6
= 332.56 cm
Answer(s): (a) 1061.32 cm
2; (b) 332.56 cm