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 + 63
Breadth of the rectangle
= 5 u
= 2 radii + 7
12 u - 5 u = (2 radii) + 63 - (2 radii + 7)
7 u = 63 - 7
7 u = 56
1 u = 56 ÷ 7 = 8
5 u = 5 x 8 = 40
Radius of the quarter circle
= (40 - 7) ÷ 2
= 33 ÷ 2
= 16.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 33
= 103.62 cm
Perimeter of the shaded part
= 103.62 + 63 + 63 + 7 + 7
= 243.62 cm
≈ 243.6 cm (Correct to 1 decimal place)
Answer(s): (a) 16.5 cm; (b) 243.6 cm