PSLE The figure is made up of 6 identical quadrants and 2 identical semicircles. The radius of each quadrant is 43 cm. The unshaded area marked A is enclosed by 2 quadrants and 2 semicircles. (Take π = 3.14)
- Find the perimeter of Z.
- Find the total shaded areas.
(a)
Perimeter of 2 semicircles
= 3.14 x 43
= 135.02 cm
Diameter of the quadrant
= 2 x 43
= 86 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 86
= 135.02 cm
Perimeter of Z
= 135.02 + 135.02
= 270.04 cm
(b)
Area of the large circle
= 3.14 x 43 x 43
= 5805.86 cm
2 Area of 2 semicircles
= 3.14 x 21.5 x 21.5
= 1451.465 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 86 x 43 -
12 x 3.14 x 43 x 43
= 3698 - 2902.93
= 795.07 cm
2 Total shaded areas
= 5805.86 - 1451.465 - 795.07
= 3559.325 cm
2 Answer(s): (a) 270.04 cm; (b) 3559.325 cm
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