Triangular Pyramid Formula

A triangular pyramid has a triangle-shaped base and all three triangular faces meet at the apex. There is a special case of a triangular pyramid called a tetrahedron, it has equilateral triangles for each of the faces. The triangular pyramid formula consists of both the volume and the surface area of the triangular pyramid that calculates the three triangular-shaped sides, the height, and the slant height. The following figure shows how a triangular pyramid looks like:

What is Triangular Pyramid Formula?

A pyramid with a triangle-shaped base whose three triangular faces meet at the apex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula: 

Volume= 1/3 × Base area ×Height

Surface Area = Base area +1/2(perimeter × slant height)

Triangular Pyramid Formula 

Formulas for volume and surface area of the triangular pyramid are: 

Volume= 1/3 × Base area ×Height

Surface Area = Base area +1/2(perimeter × slant height)

Examples Using Triangular Pyramid Formula

Example 1: Find the volume of a triangular pyramid having a base area of 10 cm² and a height of 5 cm.

Solution:

Given: base area = 10 cm², height = 5 cm.

Using the formula for the volume of a triangular pyramid

Volume =1/3 × Base area × Height

= 1/3 × 10 × 5

= 16.67 cm³

Therefore, the volume of the triangular pyramid is 16.67 cm³

Example 2: A triangular pyramid has a base area of 15 units² and a sum of the lengths of the edges 60 units. Calculate the surface area of the triangular pyramid if the slant height is 20 units.

Solution:
Given: Base area =15 units², perimeter = 60 units.

Using the formula for surface area of triangular pyramid

Surface Area = Base area + 1/2(perimeter × slant height)

= 15 + 1/2(60 × 20)
= 15 + 600
= 615 unit²

Therefore, the surface area of the triangular pyramid is 615 unit²

Example 3: Find the surface area of a triangular pyramid whose area of the base triangles is 24 square units, the perimeter of the triangle is 12 units, and the slant height of the pyramid is 18.

Solution:

The area of the base triangles = 24 squared units.

The perimeter of the triangle =12 units.

The slant height of the pyramid =18 units.

Using the formula for the surface area of a triangular pyramid

The surface area of a triangular pyramid = Base Area+ 1/2(Perimeter × Slant Height)

= 24 + 1/2 (12 × 18)

= 132 unit²

Therefore, the surface area of a triangular pyramid 132 unit²