Answer :

iGreen
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]