The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?

Dominick Blanchard
2022-05-07
Answered

The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?

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Corinne Choi

Answered 2022-05-08
Author has **15** answers

Use Thales' theorem.

You can select the points

$A=(-6,0,0),B=(+6,0,0),$

to form the longest side of the base triangle. The other point $C$ lies on a circle of which $AB$ is the diameter, as

${y}^{2}+{\textstyle [}6-x{{\textstyle ]}}^{2}+{y}^{2}+{\textstyle [}6+x{{\textstyle ]}}^{2}=144,$

so

${x}^{2}+{y}^{2}=36$

The top point $T$ is given by $(0,0,z)$ and it is clear that

$|AT|=|BT|=|CT|$

as $A$, $B$ and $C$ lie on the same circle, as $|AT|=|BT|=|AB|$, we obtain

$z=6\sqrt{3}$

You can select the points

$A=(-6,0,0),B=(+6,0,0),$

to form the longest side of the base triangle. The other point $C$ lies on a circle of which $AB$ is the diameter, as

${y}^{2}+{\textstyle [}6-x{{\textstyle ]}}^{2}+{y}^{2}+{\textstyle [}6+x{{\textstyle ]}}^{2}=144,$

so

${x}^{2}+{y}^{2}=36$

The top point $T$ is given by $(0,0,z)$ and it is clear that

$|AT|=|BT|=|CT|$

as $A$, $B$ and $C$ lie on the same circle, as $|AT|=|BT|=|AB|$, we obtain

$z=6\sqrt{3}$

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