PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 30 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of T.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 30
= 60 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 60
= 94.2 cm
Diameter of the semicircle
= 60 ÷ 3
= 20 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 20
= 94.2 cm
Perimeter of T
= 94.2 + 94.2
= 188.4 cm
(b)
Area of the large circle
= 3.14 x 30 x 30
= 2826 cm
2
Radius of 1 semicircle
= 20 ÷ 2
= 10 cm
Area of 3 semicircles
= 1
12 x 3.14 x 10 x 10
= 471 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 60 x 30 -
12 x 3.14 x 30 x 30
= 1800 - 1413
= 387 cm
2 Total shaded areas
= 2826 - 471 - 387
= 1968 cm
2 Answer(s): (a) 188.4 cm; (b) 1968 cm
2