Find by integrating the area of ​​the triangle vertices $(5,1), (1,3)\;\text{and}\;(-1,-2)$ Find by integrating the area of ​​the triangle vertices $$(5,1), (1,3)\;\text{and}\;(-1,-2)$$


I tried to make straight and integrate, but it is very complicated, there is some better way?
It is just tedious.

Let $f_1(x) = \frac{5x+1}{2}$, $f_2(x) = \frac{7-x}{2}$, $f_3(x)= \frac{x-3}{2}$.

$(-1,f_1(-1)) = (-1,f_3(-1)) = (-1,-2)$,

$(1,f_1(1)) = (1,f_2(1)) = (1,3)$,

$(5,f_2(5)) = (5, f_3(5)) = (5, 1)$.

$A = \int_{-1}^1 (f_1(x)-f_3(x) ) dx + \int_{1}^5 (f_2(x)-f_3(x) ) dx = 4 +8 = 12$.
You can try to simplify the calculations by using 1. Shift of origin ( say to (-1,-2) ), and 2. Rotation of axis. Then do the integrations.