Question

area of equilateral triangle​

Answer 1

Answer:

your answer is

Step-by-step explanation:

Area of Equilateral Triangle (A) = (√3/4)a2

Where a = length of sides

Learn more about isosceles triangles, equilateral triangles and scalene triangles here.

Derivation for Area of Equilateral Triangle

There are three methods to derive the formula for the area of equilateral triangles. They are:

Using basic triangle formula

Using rectangle construction

Using trigonometry

Deriving Area of Equilateral Triangle Using Basic Triangle Formula

Take an equilateral triangle of the side “a” units. Then draw a perpendicular bisector to the base of height “h”.



Deriving Area Of Equilateral Triangle

Now,

Area of Triangle = ½ × base × height

Here, base = a, and height = h

Now, apply Pythagoras Theorem in the triangle.

a2 = h2 + (a/2)2

⇒ h2 = a2 – (a2/4)

⇒ h2 = (3a2)/4

Or, h = ½(√3a)

Now, put the value of “h” in the area of the triangle equation.

Area of Triangle = ½ × base × height

⇒ A = ½ × a × ½(√3a)

Or, Area of Equilateral Triangle = ¼(√3a2)