PSLE The figure shows a rectangle with its corners cut out. Each of the 4 identical corners cut out is a quarter circle. The ratio of the length of the rectangle to its breadth is 13 : 5.
- What is the radius of each quarter circle?
- What is the perimeter of the shaded part. Take π = 3.14. Give your answer correct to 1 decimal place.
Length of the rectangle
= 13 u
= 2 radii + 80
Breadth of the rectangle
= 5 u
= 2 radii + 8
13 u - 5 u = (2 radii) + 80 - (2 radii + 8)
8 u = 80 - 8
8 u = 72
1 u = 72 ÷ 8 = 9
5 u = 5 x 9 = 45
Radius of the quarter circle
= (45 - 8) ÷ 2
= 37 ÷ 2
= 18.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 37
= 116.18 cm
Perimeter of the shaded part
= 116.18 + 80 + 80 + 8 + 8
= 292.18 cm
≈ 292.2 cm (Correct to 1 decimal place)
Answer(s): (a) 18.5 cm; (b) 292.2 cm