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