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 + 14
Breadth of the rectangle
= 3 u
= 2 radii + 2
5 u - 3 u = (2 radii) + 14 - (2 radii + 2)
2 u = 14 - 2
2 u = 12
1 u = 12 ÷ 2 = 6
3 u = 3 x 6 = 18
Radius of the quarter circle
= (18 - 2) ÷ 2
= 16 ÷ 2
= 8 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 16
= 50.24 cm
Perimeter of the shaded part
= 50.24 + 14 + 14 + 2 + 2
= 82.24 cm
≈ 82.2 cm (Correct to 1 decimal place)
Answer(s): (a) 8 cm; (b) 82.2 cm