PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 39 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of S.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 39
= 78 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 78
= 122.46 cm
Diameter of the semicircle
= 78 ÷ 3
= 26 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 26
= 122.46 cm
Perimeter of S
= 122.46 + 122.46
= 244.92 cm
(b)
Area of the large circle
= 3.14 x 39 x 39
= 4775.94 cm
2
Radius of 1 semicircle
= 26 ÷ 2
= 13 cm
Area of 3 semicircles
= 1
12 x 3.14 x 13 x 13
= 795.99 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 78 x 39 -
12 x 3.14 x 39 x 39
= 3042 - 2387.97
= 654.03 cm
2 Total shaded areas
= 4775.94 - 795.99 - 654.03
= 3325.92 cm
2 Answer(s): (a) 244.92 cm; (b) 3325.92 cm
2