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 7 : 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
= 7 u
= 2 radii + 29
Breadth of the rectangle
= 5 u
= 2 radii + 9
7 u - 5 u = (2 radii) + 29 - (2 radii + 9)
2 u = 29 - 9
2 u = 20
1 u = 20 ÷ 2 = 10
5 u = 5 x 10 = 50
Radius of the quarter circle
= (50 - 9) ÷ 2
= 41 ÷ 2
= 20.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 41
= 128.74 cm
Perimeter of the shaded part
= 128.74 + 29 + 29 + 9 + 9
= 204.74 cm
≈ 204.7 cm (Correct to 1 decimal place)
Answer(s): (a) 20.5 cm; (b) 204.7 cm