Question

Using herons formula find the area of an equilateral triangle if its side is 'a' units

Answer 1

S=a+a+a/2 =3a/2 A= √s(s-a)(s-b)(s-c) = √ 3a/2( 3a/2-a)(3a/2-a)(3a/2-a) = √ 3a/2( a/2)(a/2) (a/2) = a/2×a/2 √ 3 = a√3 unit^3

Answer 2

The area of equilateral triangle using heron’s formula is $\bold{=\sqrt{3} \frac{a^{2}}{4}}$.

If the side of the equilateral triangle is 'a'.

Then the area of the equilateral triangle can be found using heron’s formula

The area of a triangle is $=\sqrt{(s \times s-a \times s-b \times s-c)}$

$S =\frac{1}{2}$ (sum of sides of triangle)  

For equilateral triangle all sides are equal so that  

$S=\frac{3 a}{2}$

By substituting the value of S in the area of triangle formulae will get the area  

$=\sqrt{(s \times s-a \times s-b \times s-c)}$

$=\sqrt{\left(\frac{3 a}{2} \times\left(\frac{3 a}{2}-a\right) \times\left(\frac{3 a}{2}-a\right) \times\left(\frac{3 a}{2}-a\right)\right)}$

$=\sqrt{\left(\frac{3 a}{2} \times\left(\frac{a}{2}\right) \times\left(\frac{a}{2}\right) \times\left(\frac{a}{2}\right)\right)}$

$=\sqrt{\frac{3 a^{4}}{16}}$

$\bold{=\sqrt{3} \frac{a^{2}}{4}}$