Question

to the nearest square unit what is the area of a regular octagon with a side length of 15 and an apothem of 18.1

Answer 1

To find the area of a regular octagon, you can split the shape into eight congruent triangles from the center, find the area of one triangle, and then multiply it by eight.

If you use this method, you will find that the base of the triangle is the side length of the octagon (in this case, 15 units), and that the height is the apothem (in this case, 18.1 units).

From here, you can use the basic formula used to find the area of a triangle:
A = 1/2bh
A = 1/2 (15) (18.1)
A = 135.75 square units

Finally multiply the area of that triangle by eight.
8(135.75) = 1086 

The area of the octagon is 1086 square units.