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Why is this concept useful?: This concept can be seen in chemistry, electronics, architecture, and even art.
Where does this concept fit into the curriculum?: 5th grade

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By Puja Varude

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How to use this concept?

We can find the surface area and volume of regular tetrahedrons in the real-world.

The formula for surface area of a regular tetrahedron is:

Surface Area =

\sqrt{3} a^{2}

The formula for volume in a regular tetrahedron is:

Volume =

\frac{a^{3}}{6\sqrt{2}}

In each formula you would replace the “a” with the side length (edge).

Sample Math Problems

Question 1:

If the surface area of a regular tetrahedron is 52.6 square centimeters, what is the side length of one of its edges(Round you answer to the nearest hundredth)?

Answer:

First you would want to use the given formula and fill in the surface area.

Surface Area= √3a2

So 52.6=√3a2

Now, you need to solve the equation to find a (the side length).

Find the √3, which is 1.732

Divide each side by 1.732. This will cancel out the √3 on the right side of the equation and then you will have 52.6 divided by (1.732)=30.37

Finally you would find the square root to get a.

a=5.51

Question 2:

Find the side length of a regular tetrahedron given that the volume is 152 inches cubed (Round you answer to the nearest hundredth).

Answer:

On this problem you would want to use the given formula and fill in the

volume. Volume=

\frac{a^{3}}{6\sqrt{2}}

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Practice Math Problems

1. Find the volume of a regular tetrahedron with a side length measuring 9 units. (Round your answer to the nearest hundredth)

2. If each edge of a regular tetrahedron is 3 inches, then what is the surface area? (Round to the nearest tenth)

3. Find the side length of a regular tetrahedron with a volume of 256㎣ (Round your answer to the nearest hundredth).

4. If the surface area of a regular tetrahedron is 98.3 square centimeters, what is the side length of one of the edges(Round you answer to the nearest hundredth)?

So 152 =

\frac{a^{3}}{6\sqrt{2}}

Now, you need to solve the equation to find a (the side length). Solve 6√2 to get 8.485. Then you will multiply both sides by 8.484.

This will cancel out the 6√2 on the right side of the equation. Then you will have (8.484)(152) =

a^{3}

Next you will multiply and get 1289.72 =

a^{3}

Finally you will find the cubic root of 1289.72 to get a.

a=10.89

Question 3:

Find the volume of a regular tetrahedron with a side length measuring 7 mm. (Round your answer to the nearest hundredth)

Answer:

First you would want to use the formula and fill in s with the given side length.

Then solve for the numerator and denominator. 73=343 and 6√2 is 8.485

Finally, you would take 343 divided by 8.485= 40.4242

Don’t forget to round your answer to the nearest hundredth. So the volume

would be 40.42 ㎣

Question 4:

If the surface area of a regular tetrahedron is 52.6 square centimeters, what is the side length of one of its edges(Round you answer to the nearest hundredth)?

Answer:

First you would want to use the given formula and fill in the surface area.

Surface Area =

\sqrt{3} a^{2}

So 52.6 =

\sqrt{3} a^{2}

Now, you need to solve the equation to find a (the side length).

Find the √3, which is 1.732

Divide each side by 1.732. This will cancel out the √3 on the right side of the equation and then you will have 52.6 divided by (1.732)=30.37

Finally you would find the square root to get a.

a=5.51

Download

Geometry Worksheets

Tetrahedron

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Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Sample Math Problems

Download FREE Math Resources

8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

Practice Math Problems