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 + 12
Breadth of the rectangle
= 5 u
= 2 radii + 2
7 u - 5 u = (2 radii) + 12 - (2 radii + 2)
2 u = 12 - 2
2 u = 10
1 u = 10 ÷ 2 = 5
5 u = 5 x 5 = 25
Radius of the quarter circle
= (25 - 2) ÷ 2
= 23 ÷ 2
= 11.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 23
= 72.22 cm
Perimeter of the shaded part
= 72.22 + 12 + 12 + 2 + 2
= 100.22 cm
≈ 100.2 cm (Correct to 1 decimal place)
Answer(s): (a) 11.5 cm; (b) 100.2 cm