The area of the convex polygon is 43/2 square units
How to determine the area of the convex polygon?
The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]
So, we have:
[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]
Evaluate
[tex]A = \frac12 * (|-43|)[/tex]
Remove the absolute bracket
[tex]A = \frac12 * 43[/tex]
This gives
[tex]A = \frac{43}2[/tex]
Hence, the area of the convex polygon is 43/2 square units
Read more about convex polygon at:
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