Question

what is the volume of this triangular pyramid? 12 cm 16 cm 16 cm blank cubic centimeters submit

Explanation:

Step1: Find base triangle area

The base is an equilateral triangle with side length 16 cm. The area of a triangle is $\frac{1}{2} \times base \times height$. For the base triangle, height = $12$ cm.
$\text{Base Area} = \frac{1}{2} \times 16 \times 12 = 96$ cm²

Step2: Calculate pyramid volume

Volume of a pyramid is $\frac{1}{3} \times \text{Base Area} \times \text{Pyramid Height}$. Here, the pyramid height matches the height of the base triangle (12 cm, as the pyramid is built on this triangle with the given height as its vertical height).
$\text{Volume} = \frac{1}{3} \times 96 \times 12$

Step3: Compute final value

First calculate $96 \times 12 = 1152$, then divide by 3:
$\frac{1152}{3} = 384$

Answer:

384 cubic centimeters