Question

The polygon in the diagram is a regular octagon with center A. Find the area of the octagon to the nearest tenth of a foot. A) 22.6 ft2 B) 45.3 ft2 C) 90.5 ft2 D) 121.8 ft2
btw the radius is 4 feet.

https://www.usatestprep.com/modules/gallery/files/25/2560/2560.png
here is the picture link

Answer 1

Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore, 
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.

Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:

Area = 2√2 × r²

where r is the radius of the octagon.
Substituting the values,
We get:
             Area = 2√2 × 4²
             Area = 2√2 × 16
             Area = 2× 1.41 × 16 
             Area = 2.828 × 16 
            Area = 45.25

Rounded to the nearest tenth:

Area = 45.3 ft²