Quandaries and Queries


Question:  If a piece of property was 100 ft on the west, 133 ft on the east and 100 on the north, how many acres is this or what fraction of an acre is this property?

Do you have a formula you could pass along to us to help calculate?



Hi Elizabeth,

If the property really has only three sides, that is it is a triangle, then I can use Heron's Formula to calculate the area.

Suppose that the sides of a triangle have lengths a, b and c. Let s = (a + b + c)/2 then the area is given by

area = Sqrt[s (s - a) (s - b) (s - c)]

So your lot s = (100 + 133 + 100)/2 = 166.5 and

area = Sqrt[166.5 (66.5) (33.5) (66.5)] = 4966.5 square feet.

One acre is 43,560 square feet so your lot is

4966.5/43560 = 0.11 acres

or approximately one tenth of an acre.

If the lot has four sides then, to find the area I need the length of the fourth side and the measure of one of the angles.



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