<u>Given</u>:
Given that the height of the pyramid is 12 units.
The base of the triangle is 8 units.
The height of the triangle is 6 units.
We need to determine the volume of the pyramid.
<u>Area of the triangle:</u>
The area of the triangle can be determined using the formula,
![A=\frac{1}{2} bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20bh)
where b is the base of the triangle and h is the height of the triangle.
Substituting the values, we get;
![A=\frac{1}{2}(8)(6)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%288%29%286%29)
![A=\frac{1}{2}(48)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2848%29)
![A=24](https://tex.z-dn.net/?f=A%3D24)
Thus, the area of the triangle is 24 square units.
<u>Volume of the pyramid:</u>
The volume of the pyramid can be determined using the formula,
![V=\frac{1}{3}AH](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7DAH)
where A is the area of the triangle and H is the height of the pyramid.
Substituting the values, we get;
![V=\frac{1}{3}(24)(12)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2824%29%2812%29)
![V=\frac{1}{3}(288)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%28288%29)
![V=96](https://tex.z-dn.net/?f=V%3D96)
Thus, the volume of the pyramid is 96 cubic units.