Math CentralQuandaries & Queries


Question from carol, a student:

i have been set a question that gives a regular hexagon and each of the sloping sides is 6cm from a corner of a base to the apex(point). it also has 2cm sides
it looks sort of like this:

how do i find its height when only given those measurements?

When we asked for clarification Carol sent this drawing


Hi Carol,

It looks like you have a pyramid constructed on a base which is a regular hexagon. Look at one of the triangles that form the sides.


Q is the midpoint of one of the sides of the base so angle PQR is a right triangle. Hence you can use Pythagoras' theorem to find the length |PQ|.

Now look at the three dimensional pyramid again.


S is at the centre of the hexagonal base so |PS| is the height of the pyramid. Angle PSQ is a right angle so again you can use Pythagoras' theorem to find |PS| if you can first find |SQ|.

|SQ| is half the width of the hexagon which you can find using our response to an earlier question.


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