How do you use Heron's formula to find the area of a triangle with sides of lengths $8$ $8$ , $8$ $8$ , and $8$ $8$ ?

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Answer 1 · 2016-01-22T19:48:43

Area = 27.71 square units

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

$S = \frac{8 + 8 + 8}{2}$ $S = (8 + 8 + 8)/2$ = $\frac{24}{2}$ $24/2$ = 12

Then use Heron's Equation to calculate the area.

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

$A r e a = \sqrt{12 (12 - 8) (12 - 8) (12 - 8)}$ $Area = sqrt(12(12-8)(12-8)(12-8))$

$A r e a = \sqrt{12 (4) (4) (4)}$ $Area = sqrt(12(4)(4)(4))$

$A r e a = \sqrt{768}$ $Area = sqrt(768)$

$A r e a = 27.71 u n i t s^{2}$ $Area = 27.71 units^2$

How do you use Heron's formula to find the area of a triangle with sides of lengths 88 , 88 , and 88 ?