# using integration find the area of the region bounded by the triangle whose vertices are (-1,2),(1,5) and (3,4).

$\\line_1 \\y=\frac{5-2}{1-(-1)}(x-1)+5 \\y=\frac{3}{2}(x-1)+5 \\line_2 \\y=\frac{5-4}{1-3}(x-3)+4 \\y=-\frac{1}{2}(x-3)+4 \\line_3 \\y=\frac{4-2}{3-(-1)}(x-3)+4 \\y=\frac{1}{2}(x-4)-3 \\Now \\Area=\int_{-1}^{1}(line_1-line_3)+\int_{1}^{3}(line_2-line_3)$