Question

You have fencing material enough for a 100-yard fence. In what shape would you build the fence to get the maximum area? Why? Your answer is: (1) shape (one word); (2) Reason why you have selected this particular shape (one sentence). Possible shapes: romboid, parallelogram, triangle, pentagon, square, circle, hexagon, etc.

Answer 1

1.) Circle

2.) It gives the maximum area among others

Explanation:

Given that the fencing material = 100 yard. That means circumference = 100

Circumference of a circle = 2πr

100 = 2πr

r = 50/ π

Area of a circle = πr^2

Area of a circle = π × (50/π)^2

= 2500/ π

= 795.77 squared yard

If the area of Pentagon is calculated, we will get 688 squared yard.

Also, if the area hexagon is calculated, we will get 716 square yard