To find the area of a regular octagon, we can use the following formula:
Area = (Perimeter × Apothem) / 2
In this case, we know that the side length of the octagon is 10. Since a regular octagon has 8 equal sides, we can easily calculate the perimeter:
Perimeter = Number of Sides × Length of One Side
So, Perimeter = 8 × 10 = 80
Now, if we denote the apothem as k, we can substitute the values into the area formula:
Area = (80 × k) / 2
This simplifies to:
Area = 40k
Thus, the area of the regular octagon is 40 times the length of the apothem.
For example, if the apothem k is 5, then the area would be:
Area = 40 × 5 = 200 square units
Make sure to replace k with the actual measurement of your apothem to get the correct area of the octagon!