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 + 3
8 u - 5 u = (2 radii) + 30 - (2 radii + 3)
3 u = 30 - 3
3 u = 27
1 u = 27 ÷ 3 = 9
5 u = 5 x 9 = 45
Radius of the quarter circle
= (45 - 3) ÷ 2
= 42 ÷ 2
= 21 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 42
= 131.88 cm
Perimeter of the shaded part
= 131.88 + 30 + 30 + 3 + 3
= 197.88 cm
≈ 197.9 cm (Correct to 1 decimal place)
Answer(s): (a) 21 cm; (b) 197.9 cm