PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 45 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of C.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 45
= 90 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 90
= 141.3 cm
Diameter of the semicircle
= 90 ÷ 3
= 30 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 30
= 141.3 cm
Perimeter of C
= 141.3 + 141.3
= 282.6 cm
(b)
Area of the large circle
= 3.14 x 45 x 45
= 6358.5 cm
2
Radius of 1 semicircle
= 30 ÷ 2
= 15 cm
Area of 3 semicircles
= 1
12 x 3.14 x 15 x 15
= 1059.75 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 90 x 45 -
12 x 3.14 x 45 x 45
= 4050 - 3179.25
= 870.75 cm
2 Total shaded areas
= 6358.5 - 1059.75 - 870.75
= 4428 cm
2 Answer(s): (a) 282.6 cm; (b) 4428 cm
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