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 = sqrt(s(s-a)(s-b)(s-c))# where #s = 1/2(a+b+c)#

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

#A = sqrt(s(s-a)(s-b)(s-c))#

where #s = 1/2(a+b+c)# is the semi-perimeter.

Alternatively, if you know the three vertices #(x_1, y_1)#, #(x_2, y_2)# and #(x_3, y_3)# then the area is given by the formula:

#A = 1/2 abs(x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2)#