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 + 26
Breadth of the rectangle
= 5 u
= 2 radii + 6
7 u - 5 u = (2 radii) + 26 - (2 radii + 6)
2 u = 26 - 6
2 u = 20
1 u = 20 ÷ 2 = 10
5 u = 5 x 10 = 50
Radius of the quarter circle
= (50 - 6) ÷ 2
= 44 ÷ 2
= 22 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 44
= 138.16 cm
Perimeter of the shaded part
= 138.16 + 26 + 26 + 6 + 6
= 202.16 cm
≈ 202.2 cm (Correct to 1 decimal place)
Answer(s): (a) 22 cm; (b) 202.2 cm