Answer:
The area of the polygon is [tex]116\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of the polygon is equal to the area of the triangle ADE plus the area of triangle ACD plus the area of triangle ABC
step 1
Find the area of triangle ADE
The area is equal to
[tex]A=\frac{1}{2}(AD)(EG)[/tex]
substitute the values
[tex]A=\frac{1}{2}(16)(3)=24\ units^{2}[/tex]
step 2
Find the area of triangle ACD
The area is equal to
[tex]A=\frac{1}{2}(AD)(CH)[/tex]
substitute the values
[tex]A=\frac{1}{2}(16)(7)=56\ units^{2}[/tex]
step 3
Find the area of triangle ABC
The area is equal to
[tex]A=\frac{1}{2}(AC)(BF)[/tex]
substitute the values
[tex]A=\frac{1}{2}(12)(6)=36\ units^{2}[/tex]
step 4
Find the area of the polygon
[tex]A=24\ units^{2}+56\ units^{2}+36\ units^{2}=116\ units^{2}[/tex]
