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 + 13
Breadth of the rectangle
= 5 u
= 2 radii + 3
7 u - 5 u = (2 radii) + 13 - (2 radii + 3)
2 u = 13 - 3
2 u = 10
1 u = 10 ÷ 2 = 5
5 u = 5 x 5 = 25
Radius of the quarter circle
= (25 - 3) ÷ 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 + 13 + 13 + 3 + 3
= 101.08 cm
≈ 101.1 cm (Correct to 1 decimal place)
Answer(s): (a) 11 cm; (b) 101.1 cm