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 13 : 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
= 13 u
= 2 radii + 55
Breadth of the rectangle
= 5 u
= 2 radii + 7
13 u - 5 u = (2 radii) + 55 - (2 radii + 7)
8 u = 55 - 7
8 u = 48
1 u = 48 ÷ 8 = 6
5 u = 5 x 6 = 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 + 55 + 55 + 7 + 7
= 196.22 cm
≈ 196.2 cm (Correct to 1 decimal place)
Answer(s): (a) 11.5 cm; (b) 196.2 cm