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Identify the area of the polygon with vertices c (5, 3), a (8, -2), s (3, -4), and h (0, -2).Please help.

Identify The Area Of The Polygon With Vertices C 5 3 A 8 2 S 3 4 And H 0 2Please Help class=

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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

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