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 + 28
Breadth of the rectangle
= 7 u
= 2 radii + 4
10 u - 7 u = (2 radii) + 28 - (2 radii + 4)
3 u = 28 - 4
3 u = 24
1 u = 24 ÷ 3 = 8
7 u = 7 x 8 = 56
Radius of the quarter circle
= (56 - 4) ÷ 2
= 52 ÷ 2
= 26 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 52
= 163.28 cm
Perimeter of the shaded part
= 163.28 + 28 + 28 + 4 + 4
= 227.28 cm
≈ 227.3 cm (Correct to 1 decimal place)
Answer(s): (a) 26 cm; (b) 227.3 cm