Step 1:

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The points on the triangle region are $\"\"$ and $\"\"$ .

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Determine the centroid of the triangle formulas are : $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in above formulas.

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$\"\"$

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$\"\"$

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If $\"\"$ and $\"\"$ are the two points then the component form of vector $\"\"$ is

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$\"\"$

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If $\"\"$ and $\"\"$ are the two points then the component form of vector $\"\"$ is

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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Area $\"\"$ .

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$\"\"$

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Area $\"\"$ .

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Apply Pappus theorem: Volume $\"\"$ .

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Substitute $\"\"$ , Area $\"\"$ in above equation.

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$\"\"$

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Volume $\"\"$ .

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Solution :

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The triangle of the area $\"\"$ , and volume $\"\"$ .