The area of the polygon ABCD is 14 square units.
What is polygon?
"It is two dimensional geometric figure having finite sides and vertices."
What is formula to find the area of the polygon?
"If polygon having vertices [tex](x_1,y_1),(x_2,y_2),...,(x_n,y_n)[/tex] then the area of the polygon is,
[tex]A=\frac{1}{2}|(x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+...+(x_{n-1}y_n-x_ny_{n-1})+(x_ny_1-x_1y_n)|[/tex]
This formula is also known as shoelace formula."
For given example,
the polygon has vertices A(0, 3), B(5, 5), C(7, 3), and D(3, 1)
Consider given vertices of polygon as,
[tex](x_1,y_1)=(0,3)\\\\(x_2,y_2)=(5,5)\\\\(x_3,y_3)=(7,3)\\\\(x_4,y_4)=(3,1)[/tex]
Using the formula of area of the polygon the area of the polygon ABCD would be,
[tex]A=\frac{1}{2}|(x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+(x_3y_4-x_4y_3)+(x_4y_1-x_1y_4)|\\\\A=\frac{1}{2}|(0\times 5-5\times 3)+(5\times 3-7\times 5)+(7\times 1-3\times 3)+(3\times 3-0\times 1)|\\\\ A=\frac{1}{2}|(0-15)+(15-35)+(7-9)+(9-0)|\\\\ A=\frac{1}{2}|-15-20-2+9|\\\\ A=\frac{1}{2}\times 28\\\\ A=14~square~units[/tex]
Therefore, the area of the polygon ABCD is 14 square units.
Learn more about the area of the polygon here:
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