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

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

Equation of AB,

...(i)

Equation of BC,

y – 6 = – 1(x – 6)

y = – x + 12 ...(ii)

Equation of AC,

These are shown in the graph below: -

Clearly, Area of ΔABC = Area ADB + Area BDC

Area of ADB,

Similarly,

Thus, Area ABC = Area ADB + Area BDC

=

= 64 – 56

= 7 sq. units

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

33