We need to find the volume of the composite figure.
The volume of a rectangular pyramid having a base with dimensions a and b, and an altitude h is:
[tex]\frac{}{}\frac{a\cdot b\cdot h}{3}[/tex]
In this problem, we have:
[tex]\begin{gathered} a=12ft \\ b=10ft \\ h=3ft \end{gathered}[/tex]
Thus, the volume of the rectangular pyramid is:
[tex]\frac{12ft\cdot10ft\cdot3ft}{3}=12\cdot10\cdot\frac{3}{3}ft\cdot ft\cdot ft=120ft^3[/tex]
Now, the volume of a rectangular prism with dimensions a, b, and c, is given by:
[tex]a\cdot b\cdot c[/tex]
The lengths a and b are the same as above, and c = 7ft.
Thus, the volume of the prism is:
[tex]12ft\cdot10ft\cdot7ft=12\cdot10\cdot7ft\cdot ft\cdot ft=840ft^3[/tex]
Therefore, the volume of the composite figure is:
[tex]120ft^3+840ft^3=960ft^3[/tex]
Answer:
• Rectangular Pyramid Volume =, 120 ,ft³
• Rectangular Prism Volum = ,840, ft³
• Total Volume of Composite Figure = ,960, ft³
