How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 9, and 13 units in length?

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Answer 1 · 2016-01-23T12:54:34

$18 \sqrt{10} s q . u n i t s$ $18sqrt10sq.units$

Use Heron's formula:-
$\sqrt{s (s - a) (s - b) (s - c)}$ $sqrt(s(s-a)(s-b)(s-c)$ Where $S = \frac{a + b + c}{2}$ $S=(a+b+c)/2$

So
$a = 14, b = 9, c = 13, S = 18 =$ $a=14,b=9,c=13,S=18=$ $\frac{9 + 13 + 14}{2}$ $(9+13+14)/2$

$\to \sqrt{18 (18 - 14) (18 - 13) (18 - 9)}$ $rarrsqrt[18(18-14)(18-13)(18-9)]$

$\to \sqrt{18 (4) (5) (9)}$ $rarrsqrt[18(4)(5)(9)]$

$\to \sqrt{18 (180)}$ $rarrsqrt[18(180)]$

$\to \sqrt{3240}$ $rarrsqrt3240$

$\sqrt{3240} = 18 \sqrt{10}$ $sqrt3240=18sqrt10$