PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 42 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of X.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 42
= 84 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 84
= 131.88 cm
Diameter of the semicircle
= 84 ÷ 3
= 28 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 28
= 131.88 cm
Perimeter of X
= 131.88 + 131.88
= 263.76 cm
(b)
Area of the large circle
= 3.14 x 42 x 42
= 5538.96 cm
2
Radius of 1 semicircle
= 28 ÷ 2
= 14 cm
Area of 3 semicircles
= 1
12 x 3.14 x 14 x 14
= 923.16 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 84 x 42 -
12 x 3.14 x 42 x 42
= 3528 - 2769.48
= 758.52 cm
2 Total shaded areas
= 5538.96 - 923.16 - 758.52
= 3857.28 cm
2 Answer(s): (a) 263.76 cm; (b) 3857.28 cm
2