How to Calculate the Area of an Equilateral Triangle

Equilateral triangle with base s and height h
••• Mainland High School, MathisFun

An equilateral triangle is a triangle with all three sides of equal length. The surface area of a two dimensional polygon such as a triangle is the total area contained by the sides of the polygon. The three angles of an equilateral triangle are also of equal measure in Euclidean geometry. Since the total measure of the angles of a Euclidean triangle is 180 degrees, this means that the angles of an equilateral triangle all measure 60 degrees. The area of an equilateral triangle may be calculated when the length of one its sides is known.

    conversion of two triangle into a parallelogram

    Determine the area of a triangle when the base and height are known. Take any two identical triangles with base s and height h. We can always form a parallelogram of base s and height h with these two triangles. Since the area of a parallelogram is s x h, the area A of a triangle is therefore ½ s x h.

    Form the equilateral triangle into two right triangles with the line segment h. The hypotenuse of one of these right triangles length s, one of the legs has length h and the other leg has length s/2.

    Express h in terms of s. Using the right triangle formed in step 2, we know that s^2 = (s/2)^2 + h^2 by the Pythagorean formula. Therefore, h^2 = s^2 -- (s/2)^2 = s^2 -- s^2/4 = 3s^2/4, and we now have h = (3^1/2)s/2.

    Substitute the value of h obtained in step 3 into the formula for a triangle's area obtained in step 1. Since A = ½ s x h and h = (3^1/2)s/2, we now have A = ½ s (3^1/2)s/2 = (3^1/2)(s^2)/4.

    Use the formula for area of an equilateral triangle obtained in step 4 to find the area of an equilateral triangle with sides of length 2. A = (3^1/2)(s^2)/4 = (3^1/2)(2^2)/4 = (3^1/2).

    Things You'll Need

    • Paper
    • Pencil

Related Articles

Basic Pythagorean Theorem
How to Calculate the Length of Octagon Sides
How to Find the Area of a Parallelogram
How to Calculate a Tangent
How to Find the Missing Side of a Right Triangle
How to Solve Equations on Isosceles Triangles
Facts About Parallelograms
Formula for the Volume of a Octagon
How to Calculate the Volume and Circumference of a...
How to Find Angles in a Trapezoid
How to Measure Area
How to Figure Degrees in an Octagon
Basic Pythagorean Theorem
How to Find the Area of a Scalene Triangle
How to Find the Perimeter of a Triangle
How to Calculate the Surface Area of a Circle
How to Find a Missing Angle
How to Calculate Euclidean Distance
How to Solve Geometry Calculations
What Is a Two-Dimensional Shape?

Dont Go!

We Have More Great Sciencing Articles!