- An equilateral triangle is a triangle in which all 3 sides are equal.
- Equilateral triangles are also equiangular, which means, all three internal angles are also equal to each other and the only value possible is 60° each.
- The area of the equilateral triangle is basically the amount of space occupied by an equilateral triangle.
- The area of a triangle is measured in unit2.
- In an equilateral triangle, the median, angle bisector, and perpendicular are all the same and can be simply termed as the perpendicular bisector due to congruence conditions.
- A triangle is equilateral if and only if any 3 of the smaller triangles have either the same perimeter or the same inradius.
- A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.

**Area of Equilateral Triangle Formula: **** ****A = √3/4a ^{2}**

where “a” denoted the sides of an Equilateral Triangle

**Proof:**

In the figure above, the sides of an equilateral triangle are equal to “a” units.

We know that the area of Triangle is given by;

**A** = 1/2×base×height

To find the height, consider Triangle ABC,

Applying Pythagoras Theorem we know,

AB^{2}=AD^{2}+BD^{2}

a^{2}=h^{2}+(a/2)^{2}

h^{2}=a^{2}–a^{2}/4

h^{2}=3a^{2}/4

h=√3a/2

Thus, we can calculate area by a basic equation,

**A** = 1/2×b×h=1/2×a×√3a/2 Therefore, **A** = =√3a^{2}/4unit^{2}

**Let’s work out a few examples:-**

** Example 1:**** Find the area of an equilateral triangle whose side is 7 cm?**

** Solution:**

Given,

Side of the equilateral triangle = a = 7 cm

Area of an equilateral triangle = √3/4 a^{2}

= √3/4×72 cm^{2}

= √3/4×49 cm^{2}

= 21.21762 cm^{2}

** Example 2:** **Find the area of an equilateral triangle whose side is 28 cm?**

** Solution:**

Given,

Side of the equilateral triangle (a) = 28 cm

We know, Area of an equilateral triangle = √3/4 a^{2}

= √3/4×28^{2} cm^{2}

= √3/4×784 cm^{2}

= 339.48196 cm^{2}