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 7 : 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
= 7 u
= 2 radii + 18
Breadth of the rectangle
= 5 u
= 2 radii + 4
7 u - 5 u = (2 radii) + 18 - (2 radii + 4)
2 u = 18 - 4
2 u = 14
1 u = 14 ÷ 2 = 7
5 u = 5 x 7 = 35
Radius of the quarter circle
= (35 - 4) ÷ 2
= 31 ÷ 2
= 15.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 31
= 97.34 cm
Perimeter of the shaded part
= 97.34 + 18 + 18 + 4 + 4
= 141.34 cm
≈ 141.3 cm (Correct to 1 decimal place)
Answer(s): (a) 15.5 cm; (b) 141.3 cm