Question

question 8
this prism has a right triangle for a base. the volume of the prism is 54 cubic units. what is the value of h?
h = type your answer... units

Explanation:

Step1: Calculate the area of the base triangle

The base is a right - triangle. Using the formula for the area of a right - triangle \(A=\frac{1}{2}\times base\times height\). Here, the two legs of the right - triangle are \(3\) (using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), if \(c = 5\) and \(b=4\), then \(a=\sqrt{5^{2}-4^{2}}=\sqrt{25 - 16}=\sqrt{9}=3\)) and \(4\). So, \(A=\frac{1}{2}\times3\times4=6\) square units.

Step2: Use 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 area of the base, and \(h\) is the height (or length) of the prism. We know \(V = 54\) cubic units and \(A=6\) square units. Substituting into the formula \(54=6\times h\).

Step3: Solve for \(h\)

To find \(h\), we use the equation \(h=\frac{V}{A}\). So, \(h=\frac{54}{6}=9\) units.

Answer:

\(9\) units