Triangular Prism:
[tex]\sf~V=\dfrac{1}{2}\times~l\times~w\times~h[/tex]
[tex]\sf~V=\dfrac{1}{2}\times7\times3\times3[/tex]
[tex]\sf~V=3.5\times3\times3[/tex]
[tex]\sf~V=10.5\times3[/tex]
[tex]\sf~V=31.5[/tex]
Break the Trapezoidal Prism into a rectangular prism with side measurements of 12, 18, and 6 and into a triangular prism with measurements of 6, 16, and 12.
Rectangular Prism:
[tex]\sf~V=lwh[/tex]
[tex]\sf~V=(12)(18)(6)[/tex]
Multiply all 3 numbers together:
[tex]\sf~V=1296[/tex]
Now find the volume of the triangular prism:
[tex]\sf~V=\dfrac{1}{2}lwh[/tex]
[tex]\sf~V=\dfrac{1}{2}(6)(16)(12)[/tex]
Multiply all 4 numbers:
[tex]\sf~V=576[/tex]
Add the two volumes together:
[tex]\sf1296+576=1872[/tex]
Now we have to get rid of the area inside.
It's two rectangles both with lengths of 12 and widths of 6.
[tex]\sf~A=lw[/tex]
[tex]\sf~A=(12)(6)[/tex]
[tex]\sf~A=72[/tex]
Multiply by 2 then subtract from the total volume we got:
[tex]\sf~72\times2 = 144[/tex]
Subtract it:
[tex]\sf1872-144=1728[/tex]
