Question

Find the area of the base of regular square pyramid whose lateral faces are equilateral triangles and whose altitude is 20 cm.

Answer 1

Explanation

Step 1

draw the shape

so, An equilateral triangle is a triangle with all three sides of equal length ,

Step 2

use the pythagorean theorem to soolve for x, then

$\begin{gathered} T\mathrm{}P\text{ } \\ a^2+b^2=c^2 \\ \text{hence} \\ (\frac{x}{2})^2+20^2=x^2 \\ \frac{x^2}{4}+400^{}=x^2 \\ \frac{x^2}{4}-x^2=-400 \\ -\frac{3}{4}x^2=-400 \\ 3x^2=1600 \\ x^2=533.33 \\ x=23.09 \\ \end{gathered}$

Step 3

finally, the area of a squares is

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x