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 + 57
Breadth of the rectangle
= 5 u
= 2 radii + 8
12 u - 5 u = (2 radii) + 57 - (2 radii + 8)
7 u = 57 - 8
7 u = 49
1 u = 49 ÷ 7 = 7
5 u = 5 x 7 = 35
Radius of the quarter circle
= (35 - 8) ÷ 2
= 27 ÷ 2
= 13.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 27
= 84.78 cm
Perimeter of the shaded part
= 84.78 + 57 + 57 + 8 + 8
= 214.78 cm
≈ 214.8 cm (Correct to 1 decimal place)
Answer(s): (a) 13.5 cm; (b) 214.8 cm