Question

the bases of the prism below are right triangles. the volume of the prism is 3360 units³. find the height of the prism. 16 30 34

Explanation:

Step1: Find area of triangular base

The base is a right triangle. Using Pythagorean theorem, the third side (let's check: \(16^2 + 30^2 = 256 + 900 = 1156 = 34^2\), so legs are 16 and 30). Area of triangle \(A=\frac{1}{2}\times16\times30 = 240\) square units.

Step2: Use volume formula for prism

Volume of prism \(V = A\times h\), where \(A\) is base area, \(h\) is height of prism. Given \(V = 3360\), so \(3360 = 240\times h\). Solve for \(h\): \(h=\frac{3360}{240}=14\).

Answer:

14