According to the diagram,
Area( parallelogram ABCD) = base (height)
= 6 (1) = 6 sq. units
To find the area of rectangle BCEF, we will find length of BC and BF using distance formula
According to the diagram B(-1,3), C(-4,2) and F(1,-3)
d(BC) =
[tex] \sqrt{\left ( x2-x1 \right )^{2}+\left ( y2-y1 \right )^{2}} [/tex]
d(BC) =
[tex] \sqrt{\left ( -4-(-1) \right )^{2}+\left ( 2-3 \right )^{2}} [/tex]
d(BC) =
[tex] \sqrt{\left ( -3 \right )^{2}+\left ( -1 \right )^{2}} [/tex]
d(BC) =
[tex] \sqrt{\left 9+1\right )^{2}} [/tex]
d(BC) = = 3.16 unit
d(BF) =
[tex] \sqrt{\left (1-(-1) \right )^{2}+\left ( -3-3 \right )^{2}} [/tex]
d(BF) =
[tex] \sqrt{\left (2 \right )^{2}+\left ( -6 \right )^{2}} [/tex]
d(BF) = 6.32 unit
Area of rectangle (BCEF) = (BC)(BF)
Area of rectangle (BCEF) = (3.16)(6.32) = 19 .97 sq.units
So total area of the polygon = area of parallelogram + area of rectangle
area of the polygon = 6 + 19.97
area of the polygon = 25.97 sq.units
