Answer:
Variable B is the area of triangular base.
B = 38.5 [tex]in^{2}[/tex].
Variable h is the height of pyramid.
In the given prism, h is 9 inches.
The volume of prism is 346.5 [tex]in^{3}[/tex].
Step-by-step explanation:
Please refer to the attached image for the detailed labeling of all the sides.
[tex]\triangle ABC[/tex] is the triangular base of the prism.
BC is the base of triangular base of the prism.
AP is the height of triangular base.
Area of triangular base is represented by B and is calculated by following formula of area of a triangle.
[tex]Area = \dfrac{1}{2} \times \text{Base}\times \text{Height}[/tex]
[tex]\Rightarrow \dfrac{1}{2} \times 11 \times 7\\\Rightarrow 38.5\ in^{2}[/tex]
Hence, B = 38.5 [tex]in^{2}[/tex].
Height of prism, h = 9 in
h is represented as side BE in the attached image.
It is know that volume of prism is given as :
V = Bh
Putting values of B and h:
[tex]V = 38.5 \times 9\\\Rightarrow V = 346.5\ in^{3}[/tex]
