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 + 56
Breadth of the rectangle
= 5 u
= 2 radii + 8
13 u - 5 u = (2 radii) + 56 - (2 radii + 8)
8 u = 56 - 8
8 u = 48
1 u = 48 ÷ 8 = 6
5 u = 5 x 6 = 30
Radius of the quarter circle
= (30 - 8) ÷ 2
= 22 ÷ 2
= 11 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 22
= 69.08 cm
Perimeter of the shaded part
= 69.08 + 56 + 56 + 8 + 8
= 197.08 cm
≈ 197.1 cm (Correct to 1 decimal place)
Answer(s): (a) 11 cm; (b) 197.1 cm