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 + 57
Breadth of the rectangle
= 5 u
= 2 radii + 9
13 u - 5 u = (2 radii) + 57 - (2 radii + 9)
8 u = 57 - 9
8 u = 48
1 u = 48 ÷ 8 = 6
5 u = 5 x 6 = 30
Radius of the quarter circle
= (30 - 9) ÷ 2
= 21 ÷ 2
= 10.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 21
= 65.94 cm
Perimeter of the shaded part
= 65.94 + 57 + 57 + 9 + 9
= 197.94 cm
≈ 197.9 cm (Correct to 1 decimal place)
Answer(s): (a) 10.5 cm; (b) 197.9 cm