Answer:
A = 742.3 square units
Step-by-step explanation:
Draw the figure you have given. Draw a perpendicular from the given center point to the horizontal side above. Now you have a right triangle. The hypotenuse is 16.2.
The sum of the measures of the angles of a an n-sided polygon is
180(n - 2)
This polygon has 8 sides, so n = 8
180(n - 2) = 180(8 - 2) = 180(6) = 1080
The sum of the measures of the interior angles is 1080 deg.
There are 8 sides and 8 interior angles. Since this is a regular octagon, all sides are congruent, and all interior angles are congruent.
Each interior angle measures 1080/8 = 135 deg.
The angle on the upper right side of the right triangle is 135/2 = 67.5 deg.
For that angle, the segment you drew is the opposite leg.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
Now we find the length of half of one side of the octagon.
a^2 + b^2 = c^2
14.9668^2 + b^2 = 16.2^2
c = 6.2
Half of a side of the octagon measures 6.2; the entire side of the octagon measures 12.4.
An octagon is made up of 8 congruent triangles.
A = 8 * bh/2
A = 8 * 12.4 * 14.97/2
A = 742.3 square units