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