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# 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 cm ^{2} and a height of 5 cm.**

**Solution:**

Given: base area = 10 cm^{2}, 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 cm^{3}

Therefore, the volume of the triangular pyramid is 16.67 cm^{3}

**Example 2: A triangular pyramid has a base area of 15 units ^{2} 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 units^{2}, 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 unit^{2}

Therefore, the surface area of the triangular pyramid is 615 unit^{2}

**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 unit^{2}

Therefore, the surface area of a triangular pyramid 132 unit^{2}

## FAQs on Triangular Pyramid Formula

### What is Meant by Triangular Pyramid Formula?

A triangular pyramid has a triangle-shaped base and all 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)

### How Do You Find the Surface Area of a Triangular Pyramid?

The formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. which is Base area +1/2(perimeter × slant height). The dimensions required to find the surface area of a triangular pyramid are the side, height, and slant height.

### How Do You Find the Volume of a Triangular Pyramid?

The formula for calculating the volume of a triangular pyramid is Volume= 1/3 × Base area × Height. The dimensions required to find the surface area of a triangular pyramid are the side, height, and slant height.

### Using the Triangular Pyramid Formula, Find the Volume with a Base Area of 15 cm^{2} and a height of 4 cm.

Given: base area = 15 cm^{2}, height = 4 cm.

Using the formula for the volume of a triangular pyramid

Volume =1/3 × Base area × Height

= 1/3 × 15 × 4

= 20 cm^{3}

Therefore, the volume of the triangular pyramid is 20 cm^{3}

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