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 + 23
Breadth of the rectangle
= 7 u
= 2 radii + 5
10 u - 7 u = (2 radii) + 23 - (2 radii + 5)
3 u = 23 - 5
3 u = 18
1 u = 18 ÷ 3 = 6
7 u = 7 x 6 = 42
Radius of the quarter circle
= (42 - 5) ÷ 2
= 37 ÷ 2
= 18.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 37
= 116.18 cm
Perimeter of the shaded part
= 116.18 + 23 + 23 + 5 + 5
= 172.18 cm
≈ 172.2 cm (Correct to 1 decimal place)
Answer(s): (a) 18.5 cm; (b) 172.2 cm