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 + 29
Breadth of the rectangle
= 7 u
= 2 radii + 5
10 u - 7 u = (2 radii) + 29 - (2 radii + 5)
3 u = 29 - 5
3 u = 24
1 u = 24 ÷ 3 = 8
7 u = 7 x 8 = 56
Radius of the quarter circle
= (56 - 5) ÷ 2
= 51 ÷ 2
= 25.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 51
= 160.14 cm
Perimeter of the shaded part
= 160.14 + 29 + 29 + 5 + 5
= 228.14 cm
≈ 228.1 cm (Correct to 1 decimal place)
Answer(s): (a) 25.5 cm; (b) 228.1 cm