The formula for calculating the length of the apothem is this: the length of the side (s) divided by 2 times the tangent (tan) of 180 degrees divided by the number of sides (n).
The perimeter is 6 x 10 (n x s), equal to 60 (so p = 60). The apothem is calculated by its own formula, by plugging in 6 and 10 for n and s. The result of 2tan(180/6) is 1. 1547, and then 10 divided by 1. 1547 is equal to 8. 66. The area of the polygon is Area = a x p / 2, or 8. 66 multiplied by 60 divided by 2. The solution is an area of 259. 8 units. Note as well, there are no parenthesis in the “Area” equation, so 8. 66 divided by 2 multiplied by 60, will give you the same result, just as 60 divided by 2 multiplied by 8. 66 will give you the same result.
