How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 12, and 22 units in length?

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Answer 1 · 2016-07-17T22:32:50

$A r e a = 131.99 u n i t s^{2}$ $Area = 131.99 units^2$

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

$S = \frac{25 + 12 + 22}{2}$ $S = (25 + 12 + 22)/2$ = $\frac{59}{2}$ $59/2$ = $29.5$ $29.5$

Then use Heron's Equation to calculate the area.

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

$A r e a = \sqrt{29.5 (29.5 - 25) (29.5 - 12) (29.5 - 22)}$ $Area = sqrt(29.5(29.5-25)(29.5-12)(29.5-22))$

$A r e a = \sqrt{29.5 (4.5) (17.5) (7.5)}$ $Area = sqrt(29.5(4.5)(17.5)(7.5))$

$A r e a = \sqrt{17423.4375}$ $Area = sqrt(17423.4375)$

$A r e a = 131.99 u n i t s^{2}$ $Area = 131.99 units^2$