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 + 47
Breadth of the rectangle
= 5 u
= 2 radii + 7
13 u - 5 u = (2 radii) + 47 - (2 radii + 7)
8 u = 47 - 7
8 u = 40
1 u = 40 ÷ 8 = 5
5 u = 5 x 5 = 25
Radius of the quarter circle
= (25 - 7) ÷ 2
= 18 ÷ 2
= 9 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 18
= 56.52 cm
Perimeter of the shaded part
= 56.52 + 47 + 47 + 7 + 7
= 164.52 cm
≈ 164.5 cm (Correct to 1 decimal place)
Answer(s): (a) 9 cm; (b) 164.5 cm