Question

find the area of equilateral triangle with perimeter 180 cm by using heron's formula

Answer 1

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Answer 2

Answer:

1558.8457 square units

Step-by-step explanation:

Perimeter of equilateral triangle = $3 \times Side$

Since we are given that the perimeter of equilateral triangle is 180 cm

So, $180=3 \times Side$

$\frac{180}{3}= Side$

$60= Side$

Thus the side of the equilateral triangle is 60 cm.

Now To Find the area of the triangle using heron's formula :

a = 60 cm

b =60 cm

c = 60 cm

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

Where $s = \frac{a+b+c}{2}$

a,b,c are the side lengths of triangle  

Now substitute the values :

$s = \frac{60+60+60}{2}$

$s =90$

$Area = \sqrt{90(90-60)(90-60)(90-60)}$

$Area = 1558.8457$

Hence the area of the equilateral triangle is 1558.8457 square units