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

Step-by-step 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} \\ ((x)/(2))^2+20^2=x^2 \\ (x^2)/(4)+400^{}=x^2 \\ (x^2)/(4)-x^2=-400 \\ -(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

x