The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 4 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line X) 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 + 4
= 30 cm
Area of the big semicircle above the dotted line
= 3.14 x 30 x 30 x
12 = 1413 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
= 1413 - 1061.32
= 351.68 cm
2 Radius of the small semicircle below the dotted line
= 26 - 4
= 22 cm
Area of the small semicircle below the dotted line
= 3.14 x 22 x 22 x 26
= 351.68 cm
2 Shaded area below the dotted line
= 1061.32 - 351.68
= 709.64 cm
2 Total shaded area
= 351.68 + 709.64
= 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 + (4 x 2)
= 326.56 + 8
= 334.56 cm
Answer(s): (a) 1061.32 cm
2; (b) 334.56 cm