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 8 : 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
= 8 u
= 2 radii + 30
Breadth of the rectangle
= 5 u
= 2 radii + 6
8 u - 5 u = (2 radii) + 30 - (2 radii + 6)
3 u = 30 - 6
3 u = 24
1 u = 24 ÷ 3 = 8
5 u = 5 x 8 = 40
Radius of the quarter circle
= (40 - 6) ÷ 2
= 34 ÷ 2
= 17 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 34
= 106.76 cm
Perimeter of the shaded part
= 106.76 + 30 + 30 + 6 + 6
= 178.76 cm
≈ 178.8 cm (Correct to 1 decimal place)
Answer(s): (a) 17 cm; (b) 178.8 cm