We need to find the volume of the pyramid.
We know that the pyramid has the same base area as the prism since they have the same base: a rectangle with dimensions a and b.
Also, both the figures have the same altitude c.
The volume V₁ of the prism is given by the formula:
[tex]V_1=a\cdot b\cdot c[/tex]
And the volume V₂ of the pyramid is given by the following formula:
[tex]V_2=\frac{1}{3}\cdot a\cdot b\cdot c[/tex]
We know that the prism has a volume of 39 units³. Thus, we have:
[tex]a\cdot b\cdot c=39\text{ units}^3[/tex]
Then, using this information into the formula for the volume of the pyramid, we obtain:
[tex]V_2=\frac{1}{3}\cdot39\text{ units}^{3^{}}=13\text{ units}^3[/tex]
Therefore, the volume of the pyramid is 13 units³.
