Answer:
To find the area of the polygon with vertices C(5, 3), A(8, -2), S(3, -4), and H(0, -2).
We have that formula for finding the area of the parallelogram with n vertices is,
[tex]=\frac{1}{2}\lbrack(x1y2+x2y3+x3y4+.\ldots+xny1)-(x2y1+x3y2+x4y3+\cdots+x1yn)\rbrack[/tex]
we get that,
Area of the polygon with 4 vertices that is (x1,y1),(x2,y2),(x3,y3) and (x4,y4) is
[tex]=\frac{1}{2}\lbrack(x1y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4)\rbrack[/tex]
Substituting the values we get,
[tex]=\frac{1}{2}\lbrack(5\times(-2)+8\times(-4)+3\times(-2)+0)-(8\times3+3\times(-2)+0+5\times(-2)\rbrack[/tex][tex]=\frac{1}{2}\lbrack(-10-32-6)-(24-6-10)\rbrack[/tex][tex]=\frac{1}{2}\lbrack-48-8\rbrack[/tex][tex]=\lvert\frac{1}{2}\times(-56)\rvert[/tex][tex]=\lvert-28\rvert=28[/tex][tex]=28\text{ sq.units}[/tex]
An
