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 + 10
Breadth of the rectangle
= 5 u
= 2 radii + 2
7 u - 5 u = (2 radii) + 10 - (2 radii + 2)
2 u = 10 - 2
2 u = 8
1 u = 8 ÷ 2 = 4
5 u = 5 x 4 = 20
Radius of the quarter circle
= (20 - 2) ÷ 2
= 18 ÷ 2
= 9 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 18
= 56.52 cm
Perimeter of the shaded part
= 56.52 + 10 + 10 + 2 + 2
= 80.52 cm
≈ 80.5 cm (Correct to 1 decimal place)
Answer(s): (a) 9 cm; (b) 80.5 cm