Use the base–height formula: (A=tfrac{1}{2}bh)
Use Heron’s formula (given side lengths (a,b,c)):
(s=tfrac{a+b+c}{2})
(A=sqrt{s(s-a)(s-b)(s-c)})
Use two sides and the included angle (C): (A=tfrac{1}{2}absin C)
Use coordinates (given points ((x_1,y_1),(x_2,y_2),(x_3,y_3))):
(A=tfrac{1}{2}left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)right|)
Use right triangle legs (a,b): (A=tfrac{1}{2}ab)
Use base and two sides with included angle via law of cosines (if needed to find height or included angle):
Find the included angle (C) with (c^2=a^2+b^2-2abcos C)
Then use (A=tfrac{1}{2}absin C)