Triangle confusion

[Loki123]

I keep getting the same result over and over again. It seems correct but it's not. The reason I calculated the decimal is because the answer is in decimals so I thought to try that. Real solution is 15.2 so I still might be right but idk.

The problem is
The volume of a straight regular octagonal prism is equal to 8 cm3, and its height is sqrt2 + 1 cm. Calculate the area of the mantle.

Here is my line of thinking. I need a, so in order to calculate that, I'll use height hb and b since I can calculate both using sin45 and phytagoras. I got a, looks weird. I got M, looks weirder.

Help

 

[Steven G]

\(\displaystyle ha = h*a \neq h_a\)
If you write ha for \(\displaystyle h_a\), then you post is not readable.

 

[Loki123]

\(\displaystyle ha = h*a \neq h_a\)
If you write ha for \(\displaystyle h_a\), then you post is not readable.

Sorry about that, can't you understand from context tho?

 

[AvgStudent]

Sorry dumb question, what's a mantle?

 

[Loki123]

Sorry dumb question, what's a mantle?

Not a bad question, perhaps I translated it wrong. Basically area of the prism without both bases.

 

[AvgStudent]

Here's how I solved it, but I got 16.

 

[Loki123]

Here's how I solved it, but I got 16.
View attachment 30703

I managed to get that one way to. Close enough to 17 I say...