The area of a regular pyramid is:
[tex]Ap=\frac{1}{3}(Ab\cdot h)[/tex]
Where:
Ap = Area of the regular pyramid
Ab = Area of the basis
h = height of the pyramid
And, Ab is:
[tex]Ab=\frac{n}{2}\cdot(s\cdot a)[/tex]
Where:
n = number of sides of the polygon
s = measure of the side of the polygon
a = apothem
So, to solve this question, follow the steps below.
Step 01: Find Ab.
To find Ab, let's extract the info from the problem:
n = 6
s = 12 cm.
a = 10.4 cm.
Then,
[tex]\begin{gathered} Ab=\frac{6}{2}\cdot(12\cdot10.4) \\ Ab=3\cdot(124.8) \\ Ab=374.4cm^2 \end{gathered}[/tex]
Step 02: Use Ab to find Ap.
From the problem:
h = 36 cm.
Then,
[tex]\begin{gathered} Ap=\frac{1}{3}(374.4\cdot36) \\ Ap=4492.8cm^3 \end{gathered}[/tex]
Answer: A) 4492.8 cm³.
