A triangle has sides with lengths: 7, 12, and 15. How do you find the area of the triangle using Heron's formula?

Question

2834 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-06T21:32:56

41.23 (2 decimal places )

this is a two step process

where a , b and c represent the three sides of the triangle

$s t e p 1$ $color(red)( step 1 )$

calculate s (half of the triangles perimeter ) : $s = \frac{a + b + c}{2}$ $s = (a + b + c)/2$

in this case $s = \frac{7 + 12 + 15}{2} = \frac{34}{2} = 17$ $s = (7 + 12 +15 )/2 = 34/2 = 17$

$s t e p 2$ $color(red)(step 2 )$

calculate area : $A = \sqrt{s (s - a) (s - b) (s - c)}$ $A = sqrt( s(s - a )(s - b )(s - c )$

in this case A = $\sqrt{17 (17 - 7) (17 - 12) (17 - 15)}$ $sqrt( 17(17 - 7 )(17 - 12 )(17 - 15 )$

$\Rightarrow A = \sqrt{17 \times 10 \times 5 \times 2} = \sqrt{1700}) = 41.23$ $rArr A = sqrt (17 xx 10 xx 5 xx 2 )= sqrt1700) = 41.23$