PSLE
A symmetric figure is drawn on a rectangular piece of paper 168 cm by 105 cm as shown. Its outline consists of a large semicircle, 4 smaller semicircles and 2 straight lines.

1. What is the area of the figure?
2. What is its perimeter? Take π = 3.14

(a)
Radius of the large semicircle
= 168 ÷ 2
= 84 cm

Area of the large semicircle
= ¹₂ x 3.14 x 84 x 84
= 11077.92 cm²

Breadth of the small rectangle
= 105 - 84
= 21 cm

Area of the small rectangle
= 168 x 21
= 3528 cm²

Area of the 4 smaller semicircles
= 2 x 3.14 x 21 x 21
= 2769.48 cm²

Area of the 8 boomerangs
= 3528 - 2769.48
= 758.52 cm²

Area of the figure
= 758.52 + 11077.92
= 11836.44 cm²

(b)
Circumference of the curved lines
= 3.14 x 168
= 527.52 cm

Perimeter of the figure
= 527.52 + 21 + 21
= 569.52 cm

Answer(s): (a) 11836.44 cm²; (b) 569.52 cm