A tetrahedron is an interesting 3D figure that has four sides which are all triangles. When it is a regular tetrahedron, all these triangular surfaces resemble an equilateral triangle. To make it easier to visualize, you can consider it a three-sided pyramid. This section will show and explain the different regular tetrahedron formulas related to its surface area and its volume. You will also learn how to determine these formulas on your own. Keep on reading and understand the meaning of the symbols used in each formula.
As mentioned earlier, a regular tetrahedron is a pyramidal structure that has an equilateral triangular base. In fact, all the sides are equilateral triangles. Hence, you can easily conclude that it has 4 triangular surfaces and all the surfaces are equal in area.
On proceeding further, you can also determine the surface area of a regular tetrahedron. You have studied how to determine the area of an equilateral triangle in the previous classes. It is represented as follows.
Area of an equilateral triangle = √3a2/4 (where a = side of an equilateral triangle)
You know that the regular tetrahedron surface area formula has four such sides, it will be represented as follows.
4 (Area of an equilateral triangle) = 4(√3a2/4)
You can easily conclude that the regular tetrahedron surface area formula becomes:
Surface Area of a Regular Tetrahedron = √3a2
This is how the formula of the surface area of a regular tetrahedron is calculated easily. Understand the meaning of every formula and term associated with determining this final formula of surface area.
On further calculation by segmenting the regular tetrahedron into equilateral triangles, the altitude of this 3D shape is represented as:
h = a√6/3
Using this altitude, the regular tetrahedron volume formula is determined and represented as:
V = a3√2/12
All these formulas can be represented by just using the value of a side of the equilateral triangle. In fact, all the sides in a regular tetrahedron will be equal. This is how the regular tetrahedron volume formula is calculated. Just putting the value of 'a’ provided in the problems will give you the volume of the regular tetrahedron.
Study this section properly to find out how the different formulas of a regular tetrahedron are calculated. You will find how easy it is to figure out the surface area and the volume of the regular tetrahedron formula when you know the process. Use this concept to solve problems easily and score better in the exams.
Q1. What Does ‘a’ Stand for in a Regular Tetrahedron Formula?
Ans: The symbol ‘a’ stands for the value of one side of an equilateral triangle that forms a regular tetrahedron. All the regular tetrahedron formula is true for all values of ‘a’.
Q2. Why Should You Learn How to Determine the Volume of the Regular Tetrahedron Formula?
Ans: The prime reason for understanding the concepts of learning to determine a formula is to grasp how all the aspects are considered. In this case, we used the properties of an equilateral triangle and understood that all the surfaces and sides of a regular tetrahedron are equal.
Q3. How Can You Use the Formula of the Regular Tetrahedron?
Ans: In this section, you have learned how to use different formulas to find out the volume of the regular tetrahedron formula. It shows how you can relate the formulas of the area of 2D shapes to find the surface area and volume of 3D regular objects.