Find the area of the following polygonGiven: AC = 12, AD = 16
Accepted Solution
A:
Answer:The area of the polygon is [tex]116\ units^{2}[/tex]Step-by-step explanation:we know thatThe area of the polygon is equal to the area of the triangle ADE plus the area of triangle ACD plus the area of triangle ABCstep 1Find the area of triangle ADEThe 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 2Find the area of triangle ACDThe 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 3Find the area of triangle ABCThe 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 4Find the area of the polygon[tex]A=24\ units^{2}+56\ units^{2}+36\ units^{2}=116\ units^{2}[/tex]