Question

the volume of the given triangular prism is 8,500cm³, and its height is 40cm. what is the cross sectional area a of this prism?

Explanation:

Step1: Recall the volume formula for a prism

The volume formula for a prism is \( V = A\times h \), where \( V \) is the volume, \( A \) is the cross - sectional area, and \( h \) is the height of the prism.

Step2: Solve the formula for \( A \)

We can rewrite the formula \( V = A\times h \) to solve for \( A \). Dividing both sides of the equation by \( h \), we get \( A=\frac{V}{h} \).

Step3: Substitute the given values

We are given that \( V = 8500\space cm^{3}\) and \( h = 40\space cm\). Substituting these values into the formula \( A=\frac{V}{h} \), we have \( A=\frac{8500}{40}\).

Step4: Calculate the value of \( A \)

\( A=\frac{8500}{40}=212.5\space cm^{2}\)

Answer:

\(212.5\space cm^{2}\)