Question

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

Answer 1

To find area of ΔABC with A (4, 1), B(6, 6) and C(8, 4)

Equation of AB,

Equation of BC,

Equation of AC,

These are shown in the graph below: -

Clearly, Area of ΔABC = Area ADB + Area BDC

Area of ADB,

Thus, Area ABC = Area ADB + Area BDC

The area of the triangle ABC coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4) is 7 sq. Units.