The area of a shape is the amount of space the shape can contain. The area of polygon JKL is 24.5 square units.
Given that:
[tex]J = (-3,4)[/tex]
[tex]K =(4,4)[/tex]
[tex]L =(3,-3)[/tex]
The three vertices implies that, the polygon is a triangle.
The coordinates with the same y-axis is the base of the triangle.
This means that JK is the base.
The length of the base is the calculated using the following distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]JK = \sqrt{(-3 - 4)^2 + (4 - 4)^2}[/tex]
[tex]JK = \sqrt{49}[/tex]
[tex]JK = 7[/tex]
So, the base is:
[tex]Base = 7[/tex]
Next, we determine the height.
This is a point from any point on the base to the point on the same line as: vertex L
The point is (4, -3) --- see attachment for illustration.
So, we calculate the distance from (4,4) and (4,-3)
[tex]Height = \sqrt{(4 - 4)^2 + (4 --3)^2}[/tex]
[tex]Height = \sqrt{49}[/tex]
[tex]Height = 7[/tex]
The area is then calculated as:
[tex]Area = \frac 12 \times Base \times Height[/tex]
[tex]Area = \frac 12 \times 7 \times 7[/tex]
[tex]Area = \frac 12 \times 49[/tex]
[tex]Area = 24.5[/tex]
Hence, the area of the polygon is 24.5 square units.
Read more about areas at:
https://brainly.com/question/16418397
