PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 15 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of W.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 15
= 30 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 30
= 47.1 cm
Diameter of the semicircle
= 30 ÷ 3
= 10 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 10
= 47.1 cm
Perimeter of W
= 47.1 + 47.1
= 94.2 cm
(b)
Area of the large circle
= 3.14 x 15 x 15
= 706.5 cm
2
Radius of 1 semicircle
= 10 ÷ 2
= 5 cm
Area of 3 semicircles
= 1
12 x 3.14 x 5 x 5
= 117.75 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 30 x 15 -
12 x 3.14 x 15 x 15
= 450 - 353.25
= 96.75 cm
2 Total shaded areas
= 706.5 - 117.75 - 96.75
= 492 cm
2 Answer(s): (a) 94.2 cm; (b) 492 cm
2