The volume of the prism, in cubic units is [tex]\frac{1}{2} x^{3} + x^{2}[/tex].
The volume of a prism is defined as the total space occupied by the three-dimensional object.
volume of prism = Base area × Height
According to the given question
height = x+2
base area = area of the triangle
⇒ base area = [tex]\frac{1}{2}[/tex]×(x × x)
⇒ base area = [tex]\frac{1}{2}x^{2}[/tex]
therefore
volume of prism = [tex]\frac{1}{2} (x)^{2}(x+2)[/tex]
volume of prism = [tex]\frac{1}{2} (x^{3} +2x^{2} )[/tex]
volume of prism = [tex]\frac{1}{2} x^{3} +\frac{1}{2}(2 x^{2})[/tex]
volume of prism = [tex]\frac{1}{2}x^{3} +x^{2}[/tex]
Hence, the volume of prism, in cubic units is [tex]\frac{1}{2x^{3} } +x^{2}[/tex]
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