# Find the lateral area and volume of the right triangular prism.

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embizze | High School Teacher | (Level 1) Educator Emeritus

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(a) The volume of a prism is given by V=Bh where V is the volume, B is the area of the base, and h the height.

The base of the right triangular prism is a right triangle with legs of length 3m and 4m. The area of the base is `A=1/2(3)(4)=6"m"^2` .

The height is given as 6m.

The volume is `V=(6"m"^2)(6"m")=36"m"^3`

(b) The lateral area is the surface area minus the area of the bases.

An easy way to compute the lateral area for a right prism is LA=ph where LA is the lateral area, p is the perimeter of the base and h the height of the prism. (Note that this is just the area of each parallelogram face.)

The hypotenuse of the right traingle base is 5m. (Use the Pyhtagorean theorem if you do not recognize the Pythagorean triple.) Thus the perimeter of the base is 3m+4m+5m=12m.

Then LA=(12m)(6m)=`72"m"^2`

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