Question

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

Answer 1

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,

`=(1)/(2)\lbrack(x1y2+x2y3+x3y4+.\ldots+xny1)-(x2y1+x3y2+x4y3+\cdots+x1yn)\rbrack`

we get that,

Area of the polygon with 4 vertices that is (x1,y1),(x2,y2),(x3,y3) and (x4,y4) is

`=(1)/(2)\lbrack(x1y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4)\rbrack`

Substituting the values we get,

`=(1)/(2)\lbrack(5*(-2)+8*(-4)+3*(-2)+0)-(8*3+3*(-2)+0+5*(-2)\rbrack`
`=(1)/(2)\lbrack(-10-32-6)-(24-6-10)\rbrack`
`=(1)/(2)\lbrack-48-8\rbrack`
`=\lvert(1)/(2)*(-56)\rvert`
`=\lvert-28\rvert=28`
`=28\text{ sq.units}`

An