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 5 : 3.
- 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
= 5 u
= 2 radii + 27
Breadth of the rectangle
= 3 u
= 2 radii + 7
5 u - 3 u = (2 radii) + 27 - (2 radii + 7)
2 u = 27 - 7
2 u = 20
1 u = 20 ÷ 2 = 10
3 u = 3 x 10 = 30
Radius of the quarter circle
= (30 - 7) ÷ 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 + 27 + 27 + 7 + 7
= 140.22 cm
≈ 140.2 cm (Correct to 1 decimal place)
Answer(s): (a) 11.5 cm; (b) 140.2 cm