Find the volume of the following figure. Leave the square root in the answer. Picture in comments

Question

4everaddicted2anime · Answer

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4everaddicted2anime · Answer

The answer must be in the form:$$V=\frac{ ? }{ ? }*?\sqrt{?}$$

4everaddicted2anime · Answer

@mathmale

mathmale · Answer

I see a wedge-shaped (triangular) prism whose ends are equilateral triangles with all sides of length 3.  Could you find the area of this triangle?

mathmale · Answer

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mathmale · Answer

Before you do that, stop and think for a minute.  Do you see what I see (as described above), or have you a different interpretation?

4everaddicted2anime · Answer

I see what you see. What is the formula for finding the area of an equilateral triangle?

mathmale · Answer

Since the triangle is equilateral, the interior angles are the same.  Draw a (vertical) altitude from the uppermost vertex straight down to the base.  Label the angles (by size).
Find the length of this altitude, using the Pyth. Thm.

4everaddicted2anime · Answer

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mathmale · Answer

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4everaddicted2anime · Answer

Did I get the height of the triangle right?

mathmale · Answer

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