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 $\displaystyle A=h \frac{a+b}{2}$, 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 $\displaystyle 2*A(hexagon) + 6*A(rectangle)$, 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 $\displaystyle a$ has an area of $\displaystyle A = \frac{3\sqrt3}2a^2$. 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 $\displaystyle a$ and $\displaystyle 2a$ and heights of $\displaystyle a\sin60^\circ = a\frac{\sqrt3}2$. So, $\displaystyle A = 2\frac{(b_0 + b_1)h}2 = (a + 2a)h = 3a^2\left(\frac{\sqrt3}2\right) = \frac{3\sqrt3}2a^2$.

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

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

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

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