Question

Using integration, find the area of the triangle ABC, co-ordinates of whose vertices are A(4, 1), B(6, 6) and C(8, 4)

Answer 1

Given triangle ABC, coordinates of whose vertices are A(4, 1), B(6, 6) and C(8, 4).

Equation of AB is given by

\(y-6=\frac{6-1}{6-4}(x-6)\) or \(y=\frac{5}{2}x-9\)

Equation of BC is given by

\(y-6=\frac{4-6}{8-6}(x-8)\) or \(y = -x+12\)

Equation of AC is given by

\(y-4=\frac{4-1}{8-4}(x-8)\) or \(y=\frac{3}{4}x-2\)

\(\therefore\) Area of △ABC = area of trap. DABE + area of trap. EBCF - area of trap. DACF