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 + 71
Breadth of the rectangle
= 5 u
= 2 radii + 8
12 u - 5 u = (2 radii) + 71 - (2 radii + 8)
7 u = 71 - 8
7 u = 63
1 u = 63 ÷ 7 = 9
5 u = 5 x 9 = 45
Radius of the quarter circle
= (45 - 8) ÷ 2
= 37 ÷ 2
= 18.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 37
= 116.18 cm
Perimeter of the shaded part
= 116.18 + 71 + 71 + 8 + 8
= 274.18 cm
≈ 274.2 cm (Correct to 1 decimal place)
Answer(s): (a) 18.5 cm; (b) 274.2 cm