Question

What is the area of this polygon?
units²

5-sided polygon on a coordinate plane with vertices F, N, S, C, W. Point f is at (negative 4, negative 2), point N is at (2, 4), point s is at (5, negative 2), point c is at (5, negative 4), and point w is at (negative 4, negative 4)

Answer 1

Step 1) Draw a line from point F to point S. A rectangle forms (rectangle FSCW)

Step 2) Find the area of this rectangle. The area is 18 square units because it is 2 units high and 9 units across (9*2 = 18). You can count out the spaces or you can note how we go from x = -4 to x = 5 so subtracting the values gives -4-5 = -9 which has an absolute value of 9. 

Step 3) Find the area of triangle FSN. The base is 9 units and the height is 6 units (count out the spaces or subtract y values). So the area is A = b*h/2 = 9*6/2 = 54/2 = 27

Step 4) Add up the area of the rectangle to the area of the triangle: 18+27 = 45

Final Answer: 45 square units

note: another way to find the answer is to find the area of rectangle WABC where point A is at (-4,4) and point B is at (5,4). Then subtract off the triangular areas of AFN and BNS

Answer 2

In this exercise we have to use the knowledge of polygon area to calculate the area of ​​a trapezoid, in this way we find that:

$45 units$

So find the area of this rectangle,  this area will be:

$9*2 = 18$

Find the area of triangle FSN, this area will be:

$A = b*h/2 = 9*6/2 = 54/2 = 27$

Sum all the areas will be:

$18+27 = 45$

See more about area at brainly.com/question/1631786