PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 36 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of R.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 36
= 72 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 72
= 113.04 cm
Diameter of the semicircle
= 72 ÷ 3
= 24 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 24
= 113.04 cm
Perimeter of R
= 113.04 + 113.04
= 226.08 cm
(b)
Area of the large circle
= 3.14 x 36 x 36
= 4069.44 cm
2
Radius of 1 semicircle
= 24 ÷ 2
= 12 cm
Area of 3 semicircles
= 1
12 x 3.14 x 12 x 12
= 678.24 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 72 x 36 -
12 x 3.14 x 36 x 36
= 2592 - 2034.72
= 557.28 cm
2 Total shaded areas
= 4069.44 - 678.24 - 557.28
= 2833.92 cm
2 Answer(s): (a) 226.08 cm; (b) 2833.92 cm
2