Image credit: Desmos

Before us begin, let’s review what an equilateral triangle is — a triangle with three equal side lengths and three equal internal angles of 60° each. Now, let’s acquire one thing straight: The area of an it is intended triangle is not the perimeter that an equilateral triangle. It"s the total an are of the triangle’s surface.

You are watching: Function for the area of an equilateral triangle

As you know, over there are numerous different species of triangles: best triangles, scalene triangles, and also isosceles triangles. Again, in an it is intended triangle, the length of the political parties of an it is intended triangle room equal.

To recognize the area that an it is intended triangle, girlfriend must know its next lengths. So, prior to diving into the equilateral triangle area formula, let"s look at at just how to discover the side lengths.

## How to find the side Lengths of an it is provided Triangle

When you recognize the elevation of the triangle, you can determine the side lengths. When you"ve discovered the next length, you deserve to then identify the area of an it is intended triangle.

When you divide an it is intended triangle into two right triangles, you view the elevation of an it is intended triangle. This is excellent by slicing an equilateral triangle in half from the pointer of a vertex come the midpoint the one side to type an edge bisector.

Image credit: Desmos

The perpendicular bisector, the right line that creates two 90° angles, to represent the elevation of the it is provided triangle, as significant by height h. By producing this bisector, we’ve divided this equilateral right into two ideal triangles. To find the height, you can use the Pythagorean theorem:

Since all sides the an it is intended triangle are the same, side A=side C. And also since the base of the best triangle is half the side length of the it is provided triangle, next A=side C/2. Currently let’s plugin the height, base, and side size of C because that the hypotenuse to isolation the worth of h:

If girlfriend only know the height of an it is intended triangle’s perpendicular bisector, you deserve to use this formula to identify the length of each equal side:

Let’s use this formula to a triangle in i m sorry h = 9 to uncover the next lengths:

Now that us know exactly how to use the height of an equilateral triangle to identify its absent side length, let"s learn just how to resolve for the area.

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## Formula for the Area of it is provided Triangles

Image credit: Desmos

The figure above is an it is intended triangle. The following formula is offered to recognize the area of the triangle:

Let"s use this formula to identify the area that the triangle above:

## Mastering the Area of it is provided Triangles

Equilaterals are triangles with three equal sides and also angles the all measure 60°. As soon as you create a perpendicular bisector line through the peak of an equilateral, you type two ideal triangles. You have the right to use the Pythagorean theorem and also height of the ideal triangles in ~ the equilateral to identify the absent side lengths that an it is provided triangle.

Then, you have the right to use the formula A = √3/4 (a²) to identify the area the an it is intended triangle. Knowing how to uncover the height and area that a triangle v equal sides provides it therefore much simpler to discover other trigonometry formulas.