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 10 : 7.
- 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
= 10 u
= 2 radii + 21
Breadth of the rectangle
= 7 u
= 2 radii + 3
10 u - 7 u = (2 radii) + 21 - (2 radii + 3)
3 u = 21 - 3
3 u = 18
1 u = 18 ÷ 3 = 6
7 u = 7 x 6 = 42
Radius of the quarter circle
= (42 - 3) ÷ 2
= 39 ÷ 2
= 19.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 39
= 122.46 cm
Perimeter of the shaded part
= 122.46 + 21 + 21 + 3 + 3
= 170.46 cm
≈ 170.5 cm (Correct to 1 decimal place)
Answer(s): (a) 19.5 cm; (b) 170.5 cm