Area of Equilateral Triangle Calculator
Equilateral triangle is a triangle in which all the three sides equal. Area of Equilateral Triangle Calculator is mathematical tool to find the area of a equilateral triangle with known value of side length.
This calculator is used only when the triangle is an equilateral. In an equilateral triangle the height will cut across the middle of the triangle, forming two right triangles and dividing the base in two halves.
The area of a triangle = $\frac{1}{2} \times Base \times height$
Since all the three sides of the triangle are same, we take base = $a$
Find the altitude (height) of the triangle to the base side by using Pythagoras theorem
Height (h) = $\sqrt{AC^{2} - (\frac{BC}{2})^{2}}$
= $\sqrt{a^{2}-(\frac{a}{2})^{2}}$
= $\sqrt{a^{2}-(\frac{a^{2}}{4})}$
= $\frac{\sqrt{3}}{2}a$
The area of a equilateral triangle = $\frac{1}{2} \times Base \times height$
= $\frac{1}{2}a \times \frac{\sqrt{3}}{2}a$
= $ \frac{\sqrt{3}}{4} $$\times \ a^{2}$.
The area of a equilateral triangle = $ \frac{\sqrt{3}}{4} $$\times \ a^{2}$.
Step 1: Plug the values in the formula given above.
Step 2: Simplify the answer to obtain the area of the given equilateral triangle.
The area of a triangle = $\frac{1}{2} \times Base \times height$
Since all the three sides of the triangle are same, we take base = $a$
Find the altitude (height) of the triangle to the base side by using Pythagoras theorem
Height (h) = $\sqrt{AC^{2} - (\frac{BC}{2})^{2}}$
= $\sqrt{a^{2}-(\frac{a}{2})^{2}}$
= $\sqrt{a^{2}-(\frac{a^{2}}{4})}$
= $\frac{\sqrt{3}}{2}a$
The area of a equilateral triangle = $\frac{1}{2} \times Base \times height$
= $\frac{1}{2}a \times \frac{\sqrt{3}}{2}a$
= $ \frac{\sqrt{3}}{4} $$\times \ a^{2}$.
The area of a equilateral triangle = $ \frac{\sqrt{3}}{4} $$\times \ a^{2}$.
Step 1: Plug the values in the formula given above.
Step 2: Simplify the answer to obtain the area of the given equilateral triangle.