How To Find The Surface Area Of A Tetrahedron Pyramid

In this article, we will guide you through the process of calculating the surface area of a tetrahedron pyramid. The surface area includes the areas of all four equilateral triangular faces of the pyramid.

Step-by-Step Guide

Step 1: Show the Surface Area Formula

The surface area (SA) of a tetrahedron pyramid can be found using the following formula:

$$SA=\sqrt{3}\cdot a^2$$

Where:

- $a$ is the length of a side of the equilateral triangular faces.

Step 2: Explain the Formula

- The term $\sqrt{3}\cdot a^2$ represents the combined area of all four equilateral triangular faces of the tetrahedron.

Step 3: Insert Numbers as an Example

Let's consider a tetrahedron pyramid where the side length of each equilateral triangular face is:

- Side length: $a=5$ units

Step 4: Calculate the Final Value

First, substitute the given side length into the surface area formula:

$$SA=\sqrt{3}\cdot a^2$$

$$SA=\sqrt{3}\cdot 5^2$$

$$SA=\sqrt{3}\cdot 25$$

$$SA=25\sqrt{3}$$

Using the approximate value of $\sqrt{3}\approx 1.732$:

$$SA\approx 25\cdot 1.732$$

$$SA\approx 43.3\text{square units}$$

Final Value

The surface area of a tetrahedron pyramid with each side of the equilateral triangular faces measuring 5 units is approximately 43.3 square units.