How do you use Heron's formula to find the area of a triangle with sides of lengths $19$ $19$ , $14$ $14$ , and $13$ $13$ ?

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Answer 1 · 2016-02-04T00:57:50

The area of the triangle would be $55.3 u n i t s^{2}$ $55.3 units^2$

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First we would find S which is the sum of the 3 sides divided by 2.

$S = \frac{19 + 14 + 13}{2}$ $S = (19 + 14 + 13)/2$ = $\frac{46}{2}$ $46/2$ = $23$ $23$

Then use Heron's Equation to calculate the area.

$A r e a = \sqrt{S (S - A) (S - B) (S - C)}$ $Area = sqrt(S(S-A)(S-B)(S-C))$

$A r e a = \sqrt{23 (23 - 19) (23 - 14) (23 - 13)}$ $Area = sqrt(23(23-19)(23-14)(23-13))$

$A r e a = \sqrt{8.5 (4) (9) (10)}$ $Area = sqrt(8.5(4)(9)(10))$

$A r e a = \sqrt{3060}$ $Area = sqrt(3060)$

$A r e a = 55.3 u n i t s^{2}$ $Area = 55.3 units^2$

How do you use Heron's formula to find the area of a triangle with sides of lengths 1919 , 1414 , and 1313 ?