PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 27 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of W.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 27
= 54 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 54
= 84.78 cm
Diameter of the semicircle
= 54 ÷ 3
= 18 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 18
= 84.78 cm
Perimeter of W
= 84.78 + 84.78
= 169.56 cm
(b)
Area of the large circle
= 3.14 x 27 x 27
= 2289.06 cm
2
Radius of 1 semicircle
= 18 ÷ 2
= 9 cm
Area of 3 semicircles
= 1
12 x 3.14 x 9 x 9
= 381.51 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 54 x 27 -
12 x 3.14 x 27 x 27
= 1458 - 1144.53
= 313.47 cm
2 Total shaded areas
= 2289.06 - 381.51 - 313.47
= 1594.08 cm
2 Answer(s): (a) 169.56 cm; (b) 1594.08 cm
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