Question

1. what is the approximate volume, in in³, of a right triangular prism that is 20 inches in height and whose bases are equilateral triangles that are 4 inches on a side?

a 7
b 46
c 80
d 139

Explanation:

Step1: Find the area of the equilateral triangle base

The formula for the area of an equilateral triangle with side length \( s \) is \( A=\frac{\sqrt{3}}{4}s^{2} \). Given \( s = 4 \) inches, we substitute:
\( A=\frac{\sqrt{3}}{4}\times4^{2}=\frac{\sqrt{3}}{4}\times16 = 4\sqrt{3}\) square inches.

Step2: Calculate the volume of the triangular prism

The volume of a prism is given by \( V=Bh \), where \( B \) is the area of the base and \( h \) is the height of the prism. Here, \( B = 4\sqrt{3} \) and \( h = 20 \) inches. So:
\( V=4\sqrt{3}\times20 = 80\sqrt{3}\approx80\times1.732 = 138.56\approx139 \) cubic inches.

Answer:

139