Find the volume and total surface area of a triangular pyramid if the side of the base is 3 cm and the side edge is 10 cm.

To solve the problem, we first find the area of the base of the triangular pyramid.
To do this, we multiply the 2 sides of the pyramid and divide by 2. We get.
3 * 3/2 = 4.5 cm ^ 2.

Then, to find the volume of the pyramid, we use the following formula:
V = 1/3 * S * h
Where:
V is the volume of the pyramid;
S is the area of the base of the pyramid;
h is the height of the pyramid (apothem).
Substituting the values into the formula, we get.
V = 1/3 * 4.5 * 10 = 45 cm ^ 3.

We find the full area of the pyramid.
((p * h) / 2) + S.
p is the perimeter of the base of the pyramid. 3 + 3 + 3 = 9 cm.

((9 * 10) / 2) + 4.5 = 49.5 cm ^ 2.