54
1) Examining that shape, we can see that there is a triangle and a quadrilateral making up that shape.
2) Let's write down the coordinates of each vertex:
A(5,6)
B(11, 3)
C (11,-3)
D (4, -3)
E (5,3)
F (1,3)
2.2) Since this is an irregular polygon, then we can use the Gauss formula(a.ka. Shoelace formula) to find the Area writing matrices:
[tex]\begin{gathered} \begin{bmatrix}5 & 6 \\ 11 & 3 \\ 11 & -3 \\ 4 & -3 \\ 5 & 3 \\ 1 & 3 \\ 5 & 6\end{bmatrix} \\ \end{gathered}[/tex]
Notice that we have repeated x_1 and y_1 in the last row. We can make our "shoelace" by multiplying the diagonals this way:
[tex]\begin{gathered} A_1=\frac{1}{2}|(15-33-33+12+15+6)-(66+33-12-15+3+15)| \\ A=54 \end{gathered}[/tex]
2.4) Now, we can calculate the absolute difference between these two products:
And finally, multiply by 1/2 we got:
[tex]A=\frac{1}{2}|108|=54[/tex]
3) Thus the area is 54 square units
