Question

perimeter of an equilateral triangle is 36. find it's area using heron's formula​

Answer 1

Answer:

36√3

Step-by-step explanation:

Let the length of each side be a.

 Perimeter = 36

⇒ a + a + a = 36

⇒ 3a = 36

⇒ a = 36 / 3 ⇒ a = 12

Semi - perimeter = 36/2 = 18

Using Heron's formula:

$\mathrm{\implies Area=\sqrt{18(18-12)(18-12)(18-12) }}\\\\\implies\mathrm{Area =\sqrt{18(6)(6)(6)}}\\\\\implies\mathrm{Area =\sqrt{18\times 6 \times 6^2} }\\\\\implies\mathrm{Area=6\sqrt{18*6} }\\\\\implies\mathrm{Area=6\sqrt{6\times3 \times6} }\\\\\implies\mathrm{Area= 6*6\sqrt3 }$

    Area is 36√3