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 10 : 7.
- 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
= 10 u
= 2 radii + 36
Breadth of the rectangle
= 7 u
= 2 radii + 9
10 u - 7 u = (2 radii) + 36 - (2 radii + 9)
3 u = 36 - 9
3 u = 27
1 u = 27 ÷ 3 = 9
7 u = 7 x 9 = 63
Radius of the quarter circle
= (63 - 9) ÷ 2
= 54 ÷ 2
= 27 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 54
= 169.56 cm
Perimeter of the shaded part
= 169.56 + 36 + 36 + 9 + 9
= 259.56 cm
≈ 259.6 cm (Correct to 1 decimal place)
Answer(s): (a) 27 cm; (b) 259.6 cm