Question

Area of a eqilateral triangle whoose side is 180cm by herons formula

Answer 1

hello,

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

semi perimeter is (180+180+180)/2

s=270

s-a = 90

s-b = 90

s-c= 90

using herons formula area is:

$\sqrt{270 \times 90 \times 90 \times 90}$

$\sqrt{10 \times 10 \times 10 \times 10 \times 27 \times 9 \times 9 \times 9}$

$100 \sqrt{27 \times 9 \times 9 \times 9}$

$100 \sqrt{3 \times 9 \times 9 \times 9 \times 9}$

$100 \times 3 \times 3 \times 3 \times 3 \sqrt{3}$

$8100 \sqrt{3}$

hence area is 8100 sqrt 3

hope this helps

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Answer 2

$\huge{\underline{\underline{\red{♡Solution→}}}}$

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$\bold{\huge{\underline{\underline{\rm{ Given :}}}}}$

Sides = 180 so,

a = 180

b = 180

c = 180

$\bold{\huge{\underline{\underline{\rm{ </strong><strong>To\</strong><strong>:</strong><strong>Find</strong><strong> :}}}}}$

Area of Triangle .

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The herons formula to find Area of Triangle is :

$area(a) = \sqrt{p(p - a)(p - b)(p - c)}$

Where P is half perimeter.

$p = \frac{a + b + c}{2}$

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$\</strong><strong>p</strong><strong>u</strong><strong>r</strong><strong>p</strong><strong>l</strong><strong>e</strong><strong>{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

First find out the value of P.

$p = \frac{180 + 180 + 180}{2} \\ p = \frac{540}{2}$

$p = 270$

Now Area is ,

$a = \sqrt{270(270 - 180)(270 - 180)(270 - 180)} \\ a = \sqrt{270 \times 90 \times 90 \times 90}$

$a = \sqrt{</strong><strong>196,830,000</strong><strong>}$

$\boxed{a = 14,029.6115}$

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