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 12 : 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
= 12 u
= 2 radii + 32
Breadth of the rectangle
= 5 u
= 2 radii + 4
12 u - 5 u = (2 radii) + 32 - (2 radii + 4)
7 u = 32 - 4
7 u = 28
1 u = 28 ÷ 7 = 4
5 u = 5 x 4 = 20
Radius of the quarter circle
= (20 - 4) ÷ 2
= 16 ÷ 2
= 8 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 16
= 50.24 cm
Perimeter of the shaded part
= 50.24 + 32 + 32 + 4 + 4
= 122.24 cm
≈ 122.2 cm (Correct to 1 decimal place)
Answer(s): (a) 8 cm; (b) 122.2 cm