Frustrum base problems

[Loki123]

The basic edges of a regular octagonal frustrum are equal to 0.4 m and 0.3 m, and the height of the frustrum is equal to 0.5 m. The frustrum is completed to the full pyramid. Determine the volume of the whole pyramid.
What I am mostly struggling is the base area. How do I calculate that?
I need to know c and d. What I got is not correct is overall, very exhausting.

 

[lev888]

wolframalpha.com says the area of a regular octagon with side 40 is 7725.48, which is the same as 3200*sqrt(3+2*sqrt(2)). So the area is correct, although your solution seems too complicated. I would use trig (e.g. use tan of 22.5 to find the height, don't need c). Or just look up the formula if you don't have to derive it yourself (https://www.google.com/search?client=firefox-b-1-d&q=regular+octagon+area).

 

[Loki123]

wolframalpha.com says the area of a regular octagon with side 40 is 7725.48, which is the same as 3200*sqrt(3+2*sqrt(2)). So the area is correct, although your solution seems too complicated. I would use trig (e.g. use tan of 22.5 to find the height, don't need c). Or just look up the formula if you don't have to derive it yourself (https://www.google.com/search?client=firefox-b-1-d&q=regular+octagon+area).

how do i get tan of 22.5?

 

[BigBeachBanana]

how do i get tan of 22.5?

Do you mean without a calculator?

 

[Loki123]

Do you mean without a calculator?

Yeah

 

[lev888]

Yeah

Look up tangent of half angle.

 

[BigBeachBanana]

Yeah

You can, but you have to use a half-angle or double identity. Also, assuming you know the unit circle and radians.
[math]\tan(22.5\degree)=\tan\left(\frac{\pi}{8}\right)=\tan\left(\frac{ 1}{2}\cdot\frac{\pi}{4}\right)[/math]

 

[Loki123]

Look up tangent of half angle.

i did it that way now too. although it is simpler. I still get the same result. I need to find out how to get V=250(sqrt2+1)