1. ## Surface Area

What is the formula for the surface area of a hexagonal prism?

2. Assuming a regular hexagon....

The area of a hexagon can be found by looking at it as two trapezoids

The formula for the area of a trapeziod is $A=h \frac{a+b}{2}$, therefore the formula for the area of a hexagon is obtainable by doubling this area.

next look at the net of the shape

From this we can get the formula of the prism as $2*A(hexagon) + 6*A(rectangle)$, but this only works if all sides of the hexagon are equal

3. ## Thank you!

Thank you!

4. Originally Posted by Lpenn
What is the formula for the surface area of a hexagonal prism?
A regular hexagon of side length $a$ has an area of $A = \frac{3\sqrt3}2a^2$. This can be derived a few different ways. One way is to observe that a regular hexagon is really just two trapezoids with bases of $a$ and $2a$ and heights of $a\sin60^\circ = a\frac{\sqrt3}2$. So, $A = 2\frac{(b_0 + b_1)h}2 = (a + 2a)h = 3a^2\left(\frac{\sqrt3}2\right) = \frac{3\sqrt3}2a^2$.

A parallelogram of height $h$ and with a base of length $b$ has area $A = bh$.

Now, a hexagonal prism consists of six parallelograms and two hexagonal bases. If the base is regular, then the surface area would be

$S = 3\sqrt3a^2 + 6ah$,

where $a$ is the length of one side of the base and $h$ is the height of the prism. For non-regular bases, you will have to alter the formula.