Question

what is the volume of this triangular pyramid? 10 mm 9 mm 17 mm cubic millimeters submit

Explanation:

Step1: Calculate the base area of the triangular base

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangular base is \(b = 17\) mm and the height is \(h=9\) mm.

$$A=\frac{1}{2}\times17\times9=\frac{153}{2}\text{ mm}^2$$

Step2: Use the volume formula for a pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}\times A\times H\), where \(A\) is the base - area and \(H\) is the height of the pyramid. Here, \(H = 10\) mm and \(A=\frac{153}{2}\text{ mm}^2\)

$$V=\frac{1}{3}\times\frac{153}{2}\times10$$

First, \(\frac{1}{3}\times10=\frac{10}{3}\)

$$V=\frac{153}{2}\times\frac{10}{3}$$

\(153\div3 = 51\) and \(10\div2=5\)

$$V=51\times5$$

Answer:

\(255\)