Math CentralQuandaries & Queries


Question from Janelle:

I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off?

Hi Janelle,

One acre is 43,560 square feet so your plot is $6.5 \times 43,560 = 283,140$ square feet.

The perimeter of a triangle depends a great deal on the shape of the triangle. If all three sides are the same length $a$ feet, an equilateral triangle then its area $A$ is given by

\[A = \frac{\sqrt 3}{4} \times a^2 \mbox{ square feet.}\]

If your plot is an equilateral triangle then

\[283,140 = \frac{\sqrt 3}{4} \times a^2 \mbox{ square feet}\]

and hence

\[a^2 = \frac{4 \times 283,140}{\sqrt 3} = 653,883 \mbox{ square feet}\]


\[a = 808.6 \mbox{ feet}\]

and the amount of fencing you need is $3 \times 808.6 = 2425.9$ feet.

If your plot is not in the shape of an equilateral triangle you will need more fencing and the exact amount depends on how the lengths of the sides compare to each other.


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