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 + 41
Breadth of the rectangle
= 5 u
= 2 radii + 6
12 u - 5 u = (2 radii) + 41 - (2 radii + 6)
7 u = 41 - 6
7 u = 35
1 u = 35 ÷ 7 = 5
5 u = 5 x 5 = 25
Radius of the quarter circle
= (25 - 6) ÷ 2
= 19 ÷ 2
= 9.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 19
= 59.66 cm
Perimeter of the shaded part
= 59.66 + 41 + 41 + 6 + 6
= 153.66 cm
≈ 153.7 cm (Correct to 1 decimal place)
Answer(s): (a) 9.5 cm; (b) 153.7 cm