The term ‘**Equilateral Triangle**‘ refers to a triangle with each side equal in length. The measure of all internal angles in an equilateral triangle is 60 degrees. In a two-dimensional plane, area of an equilateral triangle is the amount of space it takes up. It is always measured in square units. As a result, an equilateral triangle is a typical example of an isosceles triangle in which all three sides are equal.

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**Area Of A Triangle**

Basically, a triangle is a three-sided polygon. It has three vertices. Angles on the interior of a triangle add up to 180°, while angles on the exterior are 360°. Triangles are of three types based on the length of their sides, isosceles triangle, **equilateral triangle**, and a right-angled triangle. Thus, the area of a triangle is equal to the total area occupied by its three sides. The **area of the triangle** is half of the base and height of the triangle.

**What Do You Mean By The Area Of An Equilateral Triangle?**

The area of a triangle is how much space it occupies in a two-dimensional plane. The equilateral triangle is a three-sided closed shape with all three sides equal and an internal angle of 60 °. It is a special case of the isosceles triangle in which the third side is also equal. If △ ABC is an equilateral triangle then AB=BC=CA and ∠A = ∠B = ∠C= 60°

**Area of an Equilateral Triangle Formula**

Triangles with three equal sides and 60° angles on all sides are known as equilateral triangles. When a perpendicular bisector line is traced through the vertex of an equilateral, two right triangles are created. By using the Pythagorean theorem and the height of right-angled triangles you can find the missing side lengths of an equilateral triangle.

The area of an equilateral triangle can be calculated using the formula given below:**Area of Equilateral Triangle (A) = √3/4 a2**

**Where a = length of sides**

**Area Of Equilateral Triangle Using Heron’s Formula**

We can use Heron’s formula to find the area of any triangle, whether it is scalene, isosceles or equilateral, provided the sides of the triangle are known.

Consider a triangle ABC whose sides are a, b, and c, respectively. An area of a triangle can therefore be calculated as follows:

Area =√((s(s-a)(s-b)(s-c)))

S is the semi-perimeter and a,b and c are the length of the sides

If it is an equilateral triangle**Area**=√(s(s-a)2^ )( since all sides are equal)

s= (a+b+c)/2= (a+a+a)/2

Therefore, **s= 3a/2**

**Examples**

**Example 1**. Find the Area of an Equilateral Triangle each of whose sides are 8 cm.

**Solution:** Given each side of an equilateral triangle = a = 8 cm.

The formula for area of an equilateral triangle = a^{2}

= ** *** 8 * 8 (cm)^{2}

= 16 cm^{2}

**Example 2**. Find the length of the side of an Equilateral Triangle with Area 9 cm^{2}

**Solution:** We know the area of equilateral triangle = ** a ^{2}**

= ** **a^{2}

Area of Equilateral Triangle is given as 9 cm^{2}

∴ 9 = ** **a^{2}

a^{2 } = 36

** **∴ a = 6

∴ The length of the side is 6 cm.

**Example 3: **Calculate the area of a triangle with a base of 12 inches and a height of 7 inches.

**Solution:**

Area of a triangle = * base(b) * height(h)

A = × b × h sq.units

⇒ A = (½) × (12 in) × (7 in)

⇒ A = (½) × (84) ( in)^{2}

⇒ A = 42 in^{2}

∴ The area of a triangle is 42 in^{2}

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**Also Read: Answer Physics Questions By Following Ncert Physics Class 11 Solutions**