PSLE The figure is made up of 6 identical quadrants and 2 identical semicircles. The radius of each quadrant is 31 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 31
= 97.34 cm
Diameter of the quadrant
= 2 x 31
= 62 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 62
= 97.34 cm
Perimeter of Z
= 97.34 + 97.34
= 194.68 cm
(b)
Area of the large circle
= 3.14 x 31 x 31
= 3017.54 cm
2 Area of 2 semicircles
= 3.14 x 15.5 x 15.5
= 754.385 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 62 x 31 -
12 x 3.14 x 31 x 31
= 1922 - 1508.77
= 413.23 cm
2 Total shaded areas
= 3017.54 - 754.385 - 413.23
= 1849.925 cm
2 Answer(s): (a) 194.68 cm; (b) 1849.925 cm
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