Question

A regular octagon with sides of length 8 and an apothem of length 9.66 has an area of _____? square units.

Answer 1

If you draw lines from the center of the octogon to each of the 8 corners, which divides the octagon into 8 triangles. Each of these triangles has a base of 8 and a height equal to the apothem, or 9.66. So the total area of the octagon is the sum of the areas of all 8 little triangles, or 8*(1/2)bh = 4(8)(9.66) = 309.12 square units.
**Note that we didn't really need the value of the apothem. If we know it's a regular octagon with a side length of 8 units, we can derive it on our own, or use some other method for finding out the area. In fact, 9.66 is only an approximation of the real length of the apothem which you can find is actually 4*cot(pi/8)). So while I do suspect our area is the "right" answer that they want, it's still not an exact value.

Answer 2

Thanks!

Answer 3

np.