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 + 17
Breadth of the rectangle
= 5 u
= 2 radii + 3
7 u - 5 u = (2 radii) + 17 - (2 radii + 3)
2 u = 17 - 3
2 u = 14
1 u = 14 ÷ 2 = 7
5 u = 5 x 7 = 35
Radius of the quarter circle
= (35 - 3) ÷ 2
= 32 ÷ 2
= 16 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 32
= 100.48 cm
Perimeter of the shaded part
= 100.48 + 17 + 17 + 3 + 3
= 140.48 cm
≈ 140.5 cm (Correct to 1 decimal place)
Answer(s): (a) 16 cm; (b) 140.5 cm