Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
There will be 8 triangles made.
The center angle will be = [tex]\frac{360}{8}=45[/tex]
The triangle will be formed an isosceles triangle, so remaining angle will be :
[tex]\frac{180-45}{2}=67.5[/tex]
[tex]sin 67.5=\frac{opposite}{5}[/tex]
opposite= CD = [tex]5sin67.5=4.6194[/tex]
Similarly,
adjacent = BD = [tex]5cos67.5=1.9134[/tex]
The complete AB will be = [tex]2*1.9134=3.8268[/tex]
Area of triangle ABC will be = [tex]\frac{1}{2}*base*height = \frac{1}{2}*3.8268*4.6194=8.838[/tex]
So, the area of octagon will be 8 times area of this triangle.
Area of octagon will be = [tex]8*8.838=70.70[/tex]
Hence are the area of octagon is 70.70 : Option D : Answer
Hope it will help :)
