Equation of line PQ is
y - 0 = \(\frac{5-0}{5-3}(x-3)\)
⇒ y = \(\frac52\)x - \(\frac{15}2\)
Equation of line QR is
y - 3 = \(\frac{5-3}{5-6}\)(x - 6)
⇒ y = -2x + 15
Equation of line PR is
y - 0 = \(\frac{3-0}{6-3}\)(x - 3)
⇒ y = x - 3
Area of ΔPQA = \(\int\limits_3^5\left[(\frac52x-\frac{15}2)-(x-3)\right]dx\)
= \(\frac34[x^2]_3^5 - \frac92[x]_3^5\)
= \(\frac34(25-9)-\frac92(5-3)\)
= \(\frac34\times16-\frac92\times2\)
= 12 - 9 = 3 square units.
Area of Δ QRA = \(\int\limits_5^6((-2x + 15)-(x-3))dx\)
\(=\int\limits_5^6(-3x + 18)dx\)
\(=-\frac32(x^2)_5^6+18(x)_5^6\)
\(=-\frac32\times11+18\)
\(=\frac{36-33}2=+\frac32\) square units (\(\because\) Area name be negative)
\(\therefore\) area of ΔABC = ar(ΔPQA) + ar(ΔQRA)
= 3 + \(\frac32=\frac92\) square units