Find the area of the $∆PQR$ whose vertices are P(4,5), Q(0,7) and R(-1,1).

Let $∆\mathrm{PQR}$ be the triangle having vertices P(4, 5), Q(0, 7), R(-1, 1).

P= (x₁, y₁) = (4, 5)

Q= (x₂, y₂) = (0, 7)

R = (x₃, y₃) = (-1, 1)

Area of $∆\mathrm{PQR}$ = $\frac{1}{2}\left|{\mathrm{x}}_1({\mathrm{y}}_{2 }– {\mathrm{y}}_3) + {\mathrm{x}}_2({\mathrm{y}}_3 – {\mathrm{y}}_1) + {\mathrm{x}}_3({\mathrm{y}}_{1 }– {\mathrm{y}}_2)\right|$

Area of $∆\mathrm{PQR}$ =$\frac{1}{2}\left|4(7-1)+0(1-5)+(-1)(5-7)\right|$
Area of $∆\mathrm{PQR}$ =$\frac{1}{2}\left|(4\times 6)+0+(-1)(-2)\right|$

Area of $∆\mathrm{PQR}$ =$\frac{1}{2}\left|24+2\right|$

Area of $∆\mathrm{PQR}$ =$\frac{1}{2}\times 26$

Area of $∆\mathrm{PQR}$ = 13 Sq. units