To find the volume of this triangular prism:
⇒ must use the formula: [tex]V = (Area_.of_.base)*height[/tex]
Let's consider the information given:
- Volume: 108 in³
- Height: 9 in
Let's plug this into the equation:
[tex]V = (Area_.of_.base) * height\\108 = (Area_.of_.base) * 9\\ (Area_.of_.base) = 12[/tex]
Now let's consider the area of the base formula
[tex]Area_.of_.base = \frac{1}{2}*triangle's_.base *triangle's_.height[/tex]
By plugging all these choices into the Area of Base's formula,
⇒ only the second choice or 4in by 6in works
[tex]Area_.of_.base = \frac{1}{2}*triangle's_.base *triangle's_.height\\Area_.of_.base = \frac{1}{2}*4*6\\ 12 = \frac{1}{2}*4*6\\12 = 12[/tex]
Answer: Second choice or 4in. by 6in.
Hope that helps!
