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 10 : 7.
- 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
= 10 u
= 2 radii + 39
Breadth of the rectangle
= 7 u
= 2 radii + 9
10 u - 7 u = (2 radii) + 39 - (2 radii + 9)
3 u = 39 - 9
3 u = 30
1 u = 30 ÷ 3 = 10
7 u = 7 x 10 = 70
Radius of the quarter circle
= (70 - 9) ÷ 2
= 61 ÷ 2
= 30.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 61
= 191.54 cm
Perimeter of the shaded part
= 191.54 + 39 + 39 + 9 + 9
= 287.54 cm
≈ 287.5 cm (Correct to 1 decimal place)
Answer(s): (a) 30.5 cm; (b) 287.5 cm