Hexagonal prism confused

[Loki123]

The problem is
The area of the larger diagonal section of a regular hexagonal prism is 24 cm2 and the circumference is 22 cm. Calculate the area and volume of the given prism.
The only thing I got correct is V1 which I find hard to believe. If I did go wrong somewhere, where?

 

[BigBeachBanana]

Where you box your equations, you have 2 equations and 2 unknowns. Use substitution or elimination. Why make things complicated?

 

[Loki123]

Where you box your equations, you have 2 equations and 2 unknowns. Use substitution or elimination. Why make things complicated?

I did use substitution. I put 11-2a instead of H in the equation 24= 2a*H

 

[BigBeachBanana]

I did use substitution. I put 11-2a instead of H in the equation 24= 2a*H

You should get a=4 and H=3

 

[Loki123]

You should get a=4 and H=3

Oh yeah, give me a sec.

 

[Loki123]

Oh yeah, give me a sec.

Now both volumes are correct! However, P1, P2 are not, in other words areas are not correct.

 

[BigBeachBanana]

 

[Loki123]

View attachment 30730
View attachment 30732

used that, but i still checked again. my answer is the same and still not correct.

 

[Deleted member 4993]

used that, but i still checked again. my answer is the same and still not correct.

I strongly suggest - start with a clean slate from the beginning.

 

[Loki123]

I strongly suggest - start with a clean slate from the beginning.

sure. give me 3 minutes

 

[Loki123]

sure. give me 3 minutes

my answer is yet again the same.

 

[BigBeachBanana]

Please show your work for area where a=4 and H=3

 

[Loki123]

Please show your work for area where a=4 and H=3

Here are all three attempts. Keep in mind, because a can have two values, I have two volumes and area. What's marked V2, P2 is the answer you are looking for.
Also A for area in the last pic.

 

[BigBeachBanana]

I can't follow your work or what you did with all the scratches. Let's go step by step and derive the formula for the area of the hexagon.
Area of regular polygon = 1/2*Perimeter*altitude
Find the altitude or the perpendicular line from the centre to one of the polygon sides.

 

[Loki123]

I can't follow your work or what you did with all the scratches. Let's go step by step and derive the formula for the area of the hexagon.
Area of regular polygon = 1/2*Perimeter*altitude
Find the altitude or the perpendicular line from the centre to one of the polygon sides.

Third one is literally the formula you sent with values 3 and 4 and it has no scratches.

 

[Loki123]

Third one is literally the formula you sent with values 3 and 4 and it has no scratches.

It's also the answer I got in all three examples. If that one is correct so is the rest.

 

[BigBeachBanana]

I used the formula and I got $27\sqrt3 + 72$

 

[Loki123]

I used the formula and I got $27\sqrt3 + 72$

How? Where I am going wrong? I even used a calculator this time.

 

[BigBeachBanana]

a is 3 not 4

 

[Loki123]

Please show your work for area where a=4 and H=3