Find the area of the polygon whose vertices are $(5,7),(9,2) and (-4,8)$

The vertices are: $(5,7),(9,2) and (-4,8)$  

Here , $(x1,y1)=(5,7)$ 

$(x2,y2)=(9,2)$ 

$(x3,y3)=(-4,8)$ 

The formula to find the area of a convex polygon is:

$\begin{array}{r}\mathrm{A}=\frac{1}{2}\mid (x1y2-x2y1)+(x2y3-x3y2)+(x3y1-x1y3)|\\ \mathrm{A}=\frac{1}{2}\left|\right(10-63)+(72+8)+(-40-28\left)\right|\\ \mathrm{A}=\frac{1}{2}|-41|\\ \mathrm{A}=\frac{1}{2}\left|41\right|\\ \mathrm{A}=\frac{41}{2}\end{array}$

Therefore, the area of the convex polygon is$\frac{41}{2}$ .