Answer:
173.82 cm^2 to the nearest hundredth.
Step-by-step explanation:
We can split it up into 8 isosceles triangles of equal area.
The base of one of these triangles = 5 cm in length.
The vertex angle is 360 / 8 = 45 degrees.
We can draw a perpendicular line from the center to form 2 right angled triangles and the 45 degree angle is split into 2 angles of 22.5 degrees and the base of these triangles is 1/2 * 6 = 3 cm.
The height of an isosceles triangle is found as follows:
tan 22.5 = 3 / h
h = 3 / tan 22.5
So the area of the isosceles triangle = (3 * 3 / tan 22.5) cm^2.
Total area of the octagon = 8 * 3 * 3 / tan 22.5
= 173.82 cm^2.
