Given:
The vertices of the polygon are (-2, -4), (4, -4), (4, 4), and (-5, 4).
Required:
We need to find the area of the given polygon.
Explanation:
Mark the points (-2, -4), (4, -4), (4, 4), and (-5, 4) and join them by line.
We get the polygons ABCD is a trapezoid.
BD is height of the trapezoid.
Let AB=a, CD=b, and BD=h.
Use the distance formula to find the measure of length.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Consider the points (-5,4) and (4,4).
[tex]Substitute\text{ }x_2=4,x_1=-5,y_2=4,\text{ and }y_1=4\text{ in the distance formula.}[/tex]
[tex]a=\sqrt{(4-(-5))^2+(4-4)^2}[/tex][tex]a=\sqrt{(4+5)^2+0}[/tex][tex]a=\sqrt{9^2}[/tex][tex]a=9units[/tex]
Consider the points (-2,-4) and (4,-4).
[tex]Substitute\text{ }x_2=4,x_1=-2,y_2=-4,\text{ and }y_1=-4\text{ in the distance formula.}[/tex]
[tex]b=\sqrt{(4-(-2))^2+(-4-(-4))^2}[/tex][tex]b=\sqrt{(4+2)^2+(-4+4)^2}[/tex][tex]b=\sqrt{6^2+0}[/tex][tex]b=6units[/tex]
Consider the points (4,4) and (4,-4).
[tex]Substitute\text{ }x_2=4,x_1=4,y_2=-4,\text{ and }y_1=4\text{ in the distance formula.}[/tex]
[tex]h=\sqrt{(4-4)^2+(-4-4)^2}[/tex][tex]h=\sqrt{0+8^2}[/tex][tex]h=8units[/tex]
Consider the area of the trapezoid formula.
[tex]A=\frac{a+b}{2}h[/tex]
Substitute a = 9 units, b = 6 units, and h =8 units in the formula.
[tex]A=\frac{9+6}{2}\cdot8[/tex][tex]A=15\cdot4[/tex][tex]A=60units^2[/tex]
Final answer:
The area of a polygon is 60 square units.
