Advanced Geometry : How to find the surface area of a tetrahedron

Example Questions

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Example Question #1 : How To Find The Surface Area Of A Tetrahedron

What is the surface area of the following tetrahedron? Assume the figure is a regular tetrahedron.

Explanation:

A tetrahedron is a three-dimensonal figure where each side is an equilateral triangle. Therefore, each angle in the triangle is .

In the figure, we know the value of the side  and the value of the base . Since dividing the triangle by half creates a  triangle, we know the value of  must be .

Therefore, the area of one side of the tetrahedron is:

Since there are four sides of a tetrahedron, the surface area is:

Example Question #2 : How To Find The Surface Area Of A Tetrahedron

A regular tetrahedron has side lengths . What is the surface area of the described solid?

Explanation:

The area of one face of the triangle can be found either through trigonometry or the Pythagorean Theorem.

Since all the sides of the triangle are , the height is then, so the area of each face is:

There are four faces, so the area of the tetrahedron is:

Example Question #3 : How To Find The Surface Area Of A Tetrahedron

Find the surface area of a regular tetrahedron with a side length of .

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Example Question #2 : How To Find The Surface Area Of A Tetrahedron

Find the surface area of a regular tetrahedron with a side length of .

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Example Question #5 : How To Find The Surface Area Of A Tetrahedron

In terms of , find the surface area of a regular tetrahedron that has a side length of .

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Example Question #6 : How To Find The Surface Area Of A Tetrahedron

In terms of , find the surface area of a regular tetrahedron with side lengths of .

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Example Question #7 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is . If the length of each side is , find the value of .

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Now, solve for .

Example Question #8 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is . If each side length is , find the value of . Round to the nearest tenths place.

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Solve for .

Example Question #9 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is . If each side length is , find the value of . Round to the nearest tenths place.

Explanation:

Use the following formula to find the surface area of a regular tetrahedron.

Now, substitute in the value of the side length into the equation.

Example Question #10 : How To Find The Surface Area Of A Tetrahedron

The surface area of a regular tetrahedron is . If each side length is , find the value of .