Answer:
[tex]\displaystyle V _{ \text{prism}} = 270 {cm}^{3} [/tex]
Step-by-step explanation:
we are given a triangular prism
we want to figure out the Volume of the given Prism
remember that,
[tex] \rm\displaystyle V _{ \text{prism}} = [\text{base area}] \times l[/tex]
since the base is triangle the formula of base area should be the formula of the area of a triangle
thus,
[tex] \rm\displaystyle V _{ \text{prism}} = [\frac{1}{2}\times b\times h] \times l[/tex]
substitute
[tex] \rm\displaystyle V _{ \text{prism}} = [\frac{1}{2}\times 9 \times 15]\times 4[/tex]
remove parentheses:
[tex] \displaystyle V _{ \text{prism}} = \frac{1}{2}\times 9\times 15\times 4[/tex]
reduce fraction:
[tex]\displaystyle V _{ \text{prism}} = 9\times 15\times 2[/tex]
simplify multiplication:
[tex]\displaystyle V _{ \text{prism}} = 270[/tex]
hence, the Volume of the given prism is 270cm³
