How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 4, and 9 units in length?

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How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 4, and 9 units in length?

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Answer 1 · 2016-01-19T12:41:21

$A = 4 \sqrt{15}$ $A=4sqrt(15)$

Explanation:

Heron's formula states the the area of a traiangle $A$ $A$ can be calculated as
$A = \sqrt{p (p - a) (p - b) (p - c)}$ $A = sqrt(p(p-a)(p-b)(p-c))$ where $p = \frac{a + b + c}{2}$ $p = (a+b+c)/2$ and $a$ $a$ , $b$ $b$ and $c$ $c$ are the three sides of the triangle.

So for this example
$p = \frac{7 + 4 + 9}{2} = 10$ $p = (7+4+9)/2 =10$

$A = \sqrt{10 (10 - 7) (10 - 4) (10 - 9)} = \sqrt{10 \cdot 4 \cdot 6 \cdot 1} = \sqrt{240}$ $A=sqrt(10(10-7)(10-4)(10-9)) = sqrt(10*4*6*1) =sqrt(240)$

$A = \sqrt{16 \cdot 15} = 4 \sqrt{15}$ $A=sqrt(16*15) = 4sqrt(15)$

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How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 4, and 9 units in length?

1 Answer

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