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Thread: Surface Area

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    Surface Area

    What is the formula for the surface area of a hexagonal prism?
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    Assuming a regular hexagon....


    The area of a hexagon can be found by looking at it as two trapezoids
    Surface Area-capture.gif

    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
    Surface Area-capture.bmp
    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
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    Thank you!

    Thank you!
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    Quote Originally Posted by Lpenn View Post
    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.
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