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−1=6−16−4(x−4) or y=52x−9
Equation of BC is given by
y−6=4−68−6(x−6) or y=−x+12
Equation of AC is given by
y−1=4−18−4(x−4) or y=34x−2
∴ Area of △ABC = area of trap. DABE + area of trap. EBCF - area of trap. DACF
= ∫64(52x−9)dx+∫86(−x+12)dx−∫84(34x−2)dx
=52[x22]64−9[x]64−[x22]86+12[x]86−34[x22]84+2[x]84
=54(36−16)−9(6−4)−12(64−36)+12(8−6)−38(64−16)+2(8−4)
=54×20−18−282+24−38×48+8
=25−18−14+24−18+8=7 sq units