ANSWER:
2362 square meters.
STEP-BY-STEP EXPLANATION:
Given:
Side = a = 30
Height = h = 36.4
s = slant length
We can calculate the lateral area of the pyramid as follows:
[tex]\begin{gathered} A_L=4\cdot\mleft(\frac{1}{2}\cdot\: a\cdot\: l\mright) \\ A_L=2\cdot a\cdot l \end{gathered}[/tex]
We can determine the inclined length by means of the Pythagorean theorem, assuming that one side is a/2 and the other side is the height.
Therefore:
[tex]\begin{gathered} A_L=2\cdot a\cdot\sqrt{\left(\frac{a}{2}\right)^2+h^2} \\ A_L=2\cdot a\cdot\sqrt[]{\frac{a}{4}+h^2} \end{gathered}[/tex]
We replacing:
[tex]\begin{gathered} A_L=2\cdot30\cdot\sqrt{\frac{30^2}{4}+\left(36.4\right)^2} \\ A_L=2362.17\cong2362m^2 \end{gathered}[/tex]
The area of the pyramid is equal to 2362 square meters.
