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 8 : 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
= 8 u
= 2 radii + 27
Breadth of the rectangle
= 5 u
= 2 radii + 6
8 u - 5 u = (2 radii) + 27 - (2 radii + 6)
3 u = 27 - 6
3 u = 21
1 u = 21 ÷ 3 = 7
5 u = 5 x 7 = 35
Radius of the quarter circle
= (35 - 6) ÷ 2
= 29 ÷ 2
= 14.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 29
= 91.06 cm
Perimeter of the shaded part
= 91.06 + 27 + 27 + 6 + 6
= 157.06 cm
≈ 157.1 cm (Correct to 1 decimal place)
Answer(s): (a) 14.5 cm; (b) 157.1 cm