Answer:
The answer is 1247.33 square inches.
Step-by-step explanation:
So you have an regular octagon.
There are 8 congruent triangles with sides of 21 inches.
First, you need to find the inside angle. The angle of the circle is 360 degrees. There are 8 congruent triangles, so you devide 360/8 and that is 45 degrees.
Then you drop an altitude from the triangle. It will divide the triangle into 2 smaller triangles with angle of 22.5 degrees.
Now you just use trigonemtric functions.
Sin(22.5 deg) = x/21
x= 21*sin(22.5 deg)
x= 8.0363 in
Cos (22.5 deg) = y/21
y= 21*(cos 22.5 deg)
y= 19.401 in
Now you use a formula for calculating the area of triangle.
(8.0363*19.401)/2=77.958 sq inches.
You just calculated area of one triangle. Octagon have 8 triangles and every one of those 8 triangles, we divided into 2 right triangles. That means, that in total, we have 16 triangles.
That is why we multiply 77.958*16
The answer is 1247.33 square inches.
I hope I helped you and I will be happy If you mark my answer as brainliest.
