Question

if each side of an equal triangle in a unit then find the aera of a triangle by using heron'& formula​

Answer 1

as side = a unit

s=( a+a+a)/2

s = 3a/2

by herons formula,

area = √s(s-a) (s-b) (s-c)

= √3a/2 (3a/2-a)(3a/2-a)(3a/2-a)

=√ 3a/2( 3a/2- a)

= √ 3a/2( 3a-a/ 2)

= √ 3a/2 x 2a/2

= √ 6a²/ 4

=√ 3 a²/2

Answer 2

Answer:

$\boxed{\text{Answer = }\frac{\sqrt{3}a^2}{4} \text{ unit}^2}$

Step-by-step explanation:

$\boxed{\text{According to Heron's Formula, Area of a Triangle: }\sqrt{s(s - a)(s - b)(s - c)}}\\\\\text{Where s = }\frac{a + b + c}{2}\\\\\text{If all sides are one unit, a = a, b = a, c = a}\\\\\text{Therefore, s = }\frac{a+a+a}{2} = \frac{3a}{2}\\\\\text{Area = }\sqrt{\frac{3a}{2} (\frac{3a}{2} - a)(\frac{3a}{2} - a)(\frac{3a}{2} - a)}\\\\= \sqrt{\frac{3a}{2}(\frac{3a}{2} - a)^3}\\\\= \sqrt{\frac{3a}{2}(\frac{a}{2})^3}\\\\= \sqrt{\frac{3a}{2} \text{ x } \frac{a^3}{8}}\\\\= \sqrt{\frac{3a^4}{16}}$

$\boxed{\text{Answer = }\frac{\sqrt{3}a^2}{4} \text{ unit}^2}$