Question

A triangular pyramid has a right triangle for its base. The perpendicular sides of the triangle are 10 inches and 18 inches long. Compute the volume of the triangular pyramid if the height is 14 inches. A) 1260 in3 B) 2520 in3 C) 252 in3 C) 420 in3

Answer 1

Check the picture below.

keeping in mind that the volume of a pyramid is one third "area of its base" times its height.

well, notice, the base triangle has itself a base of 10, and a height of 18,

$\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ height\\ -------\\ B=\frac{1}{2}(10)(18)\\ h=14 \end{cases}\implies V=\cfrac{1}{3}\left[ \frac{1}{2}(10)(18) \right](14) \\\\\\ V=(30)(14)\implies V=420$

Answer 2

Hello!

The area for a triangular pyramid is V=1/3bh. First we need to find the area of the base. The area of the triangle is half of the base and height.

b=90 in²

Now we multiply by the height.

90(14)=1260

And divide by three, or multiply by 1/3.

1260/3=420

Therefore, our answer is D) 420 in³.

I hope this helps!