## Triangle pyramid formula

A triangle pyramid is made up of a triangular base and three triangular faces that join at the apex. We come across a particular instance of a pyramid that is known as a tetrahedron. Each of its faces is an equilateral triangle.

By applying this triangular pyramid formula we can evaluate the slant height, the area of triangular shaped sides and also the height of the pyramid as it comprises both the surface area and volume of the object.

This is how a triangular pyramid appears:

From the diagram you may conclude:

A triangular pyramid includes:

A triangle-shaped base

4 vertices

6 edges

3 triangle-shaped faces

## What is the triangular pyramid formula?

This formula encompasses both the surface area and the volume of the triangular pyramid. The volume formula for a triangle-shaped pyramid measures the height and the base area, on the other hand, the surface area formula of the triangle-shaped pyramid considers the base area, slant height, and the perimeter.

In the following section we have written down the surface area and volume formulas for your reference:

Surface area = area of the triangular base + ½ (slant height x perimeter)

Volume of a triangular pyramid = 1/3 x height x base triangular area

### Solved Examples

Determine a triangular pyramid’s volume whose base area measures 12 cm2 while the height has been given as 7cm.

**Solution:** From the problem we have two following information:

Base Area = 12cm2 and height = 7cm

We have already learned about the triangular pyramid’s volume formula. Now we will apply it to solve this problem.

Volume of a triangular pyramid = 1/3 x height x base triangular area

= 1/3 x 7cm x 12cm2

= 28 cm3

**Answer:** The volume of this triangle-shaped pyramid is 28 cm3.

Calculate the triangular pyramid’s surface area whose base triangle’s area is 36 square units. The triangle’s perimeter is 18 units while its slant height measures 24.

**Solution:** The area given for the base triangle is 36 square units.

Perimeter of this triangle = 18 units.

The pyramid’s slant height = 24 units.

All we need to do is substitute the values in the standard formula meant for calculating a triangular pyramid’s surface area.

Surface area of this triangular pyramid = area of the triangular base + ½ (slant height x perimeter)

= 36 + ½ (24 x 18)

= 36 + ½ x 432

= 252 unit2

**Answer:** The triangular pyramid’s surface area is 252 unit2.