PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 48 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of B.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 48
= 96 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 96
= 150.72 cm
Diameter of the semicircle
= 96 ÷ 3
= 32 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 32
= 150.72 cm
Perimeter of B
= 150.72 + 150.72
= 301.44 cm
(b)
Area of the large circle
= 3.14 x 48 x 48
= 7234.56 cm
2
Radius of 1 semicircle
= 32 ÷ 2
= 16 cm
Area of 3 semicircles
= 1
12 x 3.14 x 16 x 16
= 1205.76 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 96 x 48 -
12 x 3.14 x 48 x 48
= 4608 - 3617.28
= 990.72 cm
2 Total shaded areas
= 7234.56 - 1205.76 - 990.72
= 5038.08 cm
2 Answer(s): (a) 301.44 cm; (b) 5038.08 cm
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