An Easy Heron's Formula

Geometry Level 2

Find the area of triangle with sides 17 , 25 , and 26 ?


The answer is 204.

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1 solution

Sravanth C.
Apr 22, 2015

We know the herons formula is s ( s a ) ( s b ) ( s ) \sqrt{s(s-a)(s-b)(s-)}

Here s = 17 + 25 + 26 2 = 34 \displaystyle s=\frac{17+25+26}{2} = 34

a = 17 , b = 25 , c = 26 a=17, b=25, c=26

Therefore the area of the triangle is,

34 ( 34 17 ) ( 34 25 ) ( 34 26 ) \sqrt{34(34-17)(34-25)(34-26)}

Or, ( 34 ) × ( 17 ) × ( 9 ) × ( 8 ) \sqrt{(34)\times(17)\times(9)\times(8)}

Or, 17 × 2 × 17 × 3 × 3 × 2 × 2 × 2 \sqrt{17\times2\times17\times3\times3\times2\times2\times2}

Or, 204 × 204 \sqrt{204\times204}

Or, 204 \boxed{204}

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