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| Math Central | Quandaries & Queries |
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Question from ele, a student: On square based pyramid, the lengths of the sides of the base are all 2m. The height from the top of the pyramid to the middle of the base is 0.5m. What are the lengths of the sides of the triangular pieces and the contained angle? |
Hi Ele,
In the solution to this problem you get to use Pythagoras' theorem many times.
In my diagram the square base of the pyramid is $ABCD$ and the apex is $P.$ $E$ is the midpoint of $BD$ and $F$ is the midpoint of $BC.$
$ABD$ is a right triangle and $|AB| = |DA| = 2$ m. What is the length of $BD?$
What is the length |$BE|?$
$EBP$ is a right triangle. What is the length $|PB|?$
$FPB$ is a right triangle. What is the length $|FP|?$ What is the measure of the angle $EFP?$
Penny
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