Question

what is the volume of this triangular pyramid? 45 mm 60 mm 46 mm cubic millimeters

Explanation:

Step1: Find base - area of the triangular base

The base of the triangular pyramid is a right - triangle with legs \(a = 60\) mm and \(b = 46\) mm. The area of a right - triangle \(A=\frac{1}{2}ab\). So, \(A=\frac{1}{2}\times60\times46 = 1380\) \(mm^{2}\).

Step2: Calculate the volume of the pyramid

The volume of a pyramid \(V=\frac{1}{3}Ah\), where \(A\) is the base - area and \(h\) is the height. Here, \(A = 1380\) \(mm^{2}\) and \(h = 45\) mm. Then \(V=\frac{1}{3}\times1380\times45\). First, \(\frac{1}{3}\times1380 = 460\), and \(460\times45=20700\) \(mm^{3}\).

Answer:

20700