The area of the pentagon is 19 square units
The coordinates of the pentagon are given as:
[tex]T = (1, 8)[/tex]
[tex]E =(3, 8)[/tex]
[tex]X =(6, 2)[/tex]
[tex]A=(3, 2)[/tex]
[tex]S = (1, 4)[/tex]
The area of the pentagon is then calculated using:
[tex]Area = \frac 12|(x_1y_2+x_2y_3+x_3y_4+x_4y_5+x_5y_1) -(y_1x_2+y_2x_3+y_3x_4+y_4x_5+y_5x_1)|[/tex]
So, we have:
[tex]Area = \frac 12|(1 \times 8 +3 \times 2+6\times2+3 \times 4 + 1 \times 8) -(8\times3+8\times6+2\times3+2\times1+4\times1)|[/tex]
Simplify the expressions in both brackets
[tex]Area = \frac 12|46 -84|[/tex]
[tex]Area = \frac 12|-38|[/tex]
Remove absolute bracket
[tex]Area = \frac 12 \times 38[/tex]
[tex]Area = 19[/tex]
Hence, the area of the pentagon is 19 square units
Read more about areas at:
https://brainly.com/question/1423568
