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QuestionCalculate the volume of a triangular prism with side lengths of 8yd, 10yd, and 12yd.

Studdy Solution

STEP 1

Assumptions1. The triangular prism is a right-angled triangular prism. The sides of the triangle are8yd,10yd, and12yd3. The longest side (12yd) is the hypotenuse of the triangle, and the other two sides (8yd and10yd) are the base and height of the triangle respectively.

STEP 2

The volume of a triangular prism can be found using the formulaVolume=12×Base×Height×LengthVolume = \frac{1}{2} \times Base \times Height \times Length

STEP 3

In this case, the base and height of the triangle are8yd and10yd respectively. The length of the prism is the hypotenuse of the triangle, which is12yd.Substitute these values into the formulaVolume=12×8yd×10yd×12ydVolume = \frac{1}{2} \times8yd \times10yd \times12yd

STEP 4

Now, calculate the volume of the triangular prismVolume=12×8yd×10yd×12yd=480yd3Volume = \frac{1}{2} \times8yd \times10yd \times12yd =480yd^3The volume of the triangular prism is480 cubic yards.

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