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 + 58
Breadth of the rectangle
= 5 u
= 2 radii + 9
12 u - 5 u = (2 radii) + 58 - (2 radii + 9)
7 u = 58 - 9
7 u = 49
1 u = 49 ÷ 7 = 7
5 u = 5 x 7 = 35
Radius of the quarter circle
= (35 - 9) ÷ 2
= 26 ÷ 2
= 13 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 26
= 81.64 cm
Perimeter of the shaded part
= 81.64 + 58 + 58 + 9 + 9
= 215.64 cm
≈ 215.6 cm (Correct to 1 decimal place)
Answer(s): (a) 13 cm; (b) 215.6 cm