How Do You Find the Area of an Octagon?

To calculate the area of an octagon, substitute the length of one side for s in the formula: area = 2 * s^2 * (1+?2). If the side is measured in centimeters, then the total area is expressed as centimeters squared.

  1. Plug a side measurement into the formula

    For example, if one side of an octagon measures 10 centimeters, substitute 10 for s in the formula to give area = 2 * 10^2 * (1+?2).

  2. Solve according to the order of operations

    First calculate 10^2 by multiplying 10 by 10. Ten squared equals 100, so the formula now reads: area = 2 * 100 * (1+?2). Next, multiply two times 100, which equals 200, to give area = 200 * (1+?2). Calculate 1+?2. The square root of two is 1.414 so 1 + 1.414 = 2.414. Finally, multiply 200 by 2.414, which equals 482.8.

  3. Add the correct units of measurement

    The original side has a measurement expressed in centimeters so the area is also expressed in centimeters. Unlike length, area is expressed in square units. The correct unit of measurement for the answer in the example is therefore centimeters squared. The complete answer to the example is that the area of an octagon with sides of length 10 centimeters is 482.8 centimeters squared.