What is the formula for the area of a non right-angled triangle?

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What is the formula for the area of a non right-angled triangle?

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Answer 1 · 2018-06-17T14:17:44

For a triangle with sides $a, b, c$ $a, b, c$ :

$A = \sqrt{s (s - a) (s - b) (s - c)}$ $A = sqrt(s(s-a)(s-b)(s-c))$ where $s = \frac{1}{2} (a + b + c)$ $s = 1/2(a+b+c)$

Explanation:

Assuming you know the lengths $a, b, c$ $a, b, c$ of the three sides, then you can use Heron's formula:

$A = \sqrt{s (s - a) (s - b) (s - c)}$ $A = sqrt(s(s-a)(s-b)(s-c))$

where $s = \frac{1}{2} (a + b + c)$ $s = 1/2(a+b+c)$ is the semi-perimeter.

Alternatively, if you know the three vertices $(x_{1}, y_{1})$ $(x_1, y_1)$ , $(x_{2}, y_{2})$ $(x_2, y_2)$ and $(x_{3}, y_{3})$ $(x_3, y_3)$ then the area is given by the formula:

$A = \frac{1}{2} | x_{1} y_{2} + x_{2} y_{3} + x_{3} y_{1} - x_{1} y_{3} - x_{2} y_{1} - x_{3} y_{2} |$ $A = 1/2 abs(x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2)$

(see https://socratic.org/s/aRRwRfUE)

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What is the formula for the area of a non right-angled triangle?

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