To find the area of the base of a pyramid with a square base, we can start with the formula for the volume of a pyramid.
The volume [tex]\( V \)[/tex] of a pyramid with a square base is given by the formula:
[tex]\[ V = \frac{1}{3} \times (\text{Area of the base}) \times (\text{height}) \][/tex]
Let:
- [tex]\( A \)[/tex] be the area of the square base,
- [tex]\( h \)[/tex] be the height of the pyramid,
- [tex]\( V \)[/tex] be the volume of the pyramid.
The formula for the volume thus becomes:
[tex]\[ V = \frac{1}{3} \times A \times h \][/tex]
To find the area of the base, we need to solve this equation for [tex]\( A \)[/tex]. Start by multiplying both sides of the equation by 3 to get rid of the fraction:
[tex]\[ 3V = A \times h \][/tex]
Next, divide both sides of the equation by the height [tex]\( h \)[/tex] to isolate [tex]\( A \)[/tex]:
[tex]\[ A = \frac{3V}{h} \][/tex]
So, the expression that represents the area of the base of the pyramid is:
[tex]\[ \frac{3V}{h} \][/tex]
Therefore, the correct choice from the given options is:
[tex]\[ \frac{3V}{h} \, \text{units}^2 \][/tex]
