Question - Calculating Volume of Triangular Pyramid
Solution:
The volume $$ V $$ of a pyramid can be calculated using the formula:\[ V = \frac{1}{3} B h \]where $$ B $$ is the area of the base and $$ h $$ is the height of the pyramid. Here, the base is a triangle with a base of 6 inches and a height of 4 inches. First, calculate the area of the triangular base $$ A $$:\[ A = \frac{1}{2} base \times height = \frac{1}{2} \times 6 \times 4 \]\[ A = 3 \times 4 \]\[ A = 12 \, \text{in}^2 \]Next, use the triangular base area and the height of the pyramid (7 inches) to find the volume:\[ V = \frac{1}{3} \times 12 \times 7 \]\[ V = 4 \times 7 \]\[ V = 28 \, \text{cubic inches} \]So, the volume of the triangular pyramid is 28 cubic inches.
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