Question

HELP!

A regular octagon is inscribed in a circle with a radius of 5 feet. What is the area of the octagon?

A) 72.3
B) 76.5
C) 71.5
D) 70.7

Answer 1

the answer is d I know this one

Answer 2

Explanation:

Alright, lets get started.

Please refer the diagram I have attached.

There will be 8 triangles made.

The center angle will be =
`(360)/(8)=45`

The triangle will be formed an isosceles triangle, so remaining angle will be :

`(180-45)/(2)=67.5`

`sin 67.5=(opposite)/(5)`

opposite= CD =
`5sin67.5=4.6194`

Similarly,

adjacent = BD =
`5cos67.5=1.9134`

The complete AB will be =
`2*1.9134=3.8268`

Area of triangle ABC will be =
`(1)/(2)*base*height = (1)/(2)*3.8268*4.6194=8.838`

So, the area of octagon will be 8 times area of this triangle.

Area of octagon will be =
`8*8.838=70.70`

Hence are the area of octagon is 70.70 : Option D : Answer

Hope it will help :)