Question

Find the area of the following polygon


Given: AC = 12, AD = 16

Answer 1

The area of the polygon is
`116\ units^(2)`

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

`A=(1)/(2)(AD)(EG)`

substitute the values

`A=(1)/(2)(16)(3)=24\ units^(2)`

step 2

Find the area of triangle ACD

The area is equal to

`A=(1)/(2)(AD)(CH)`

substitute the values

`A=(1)/(2)(16)(7)=56\ units^(2)`

step 3

Find the area of triangle ABC

The area is equal to

`A=(1)/(2)(AC)(BF)`

substitute the values

`A=(1)/(2)(12)(6)=36\ units^(2)`

step 4

Find the area of the polygon

`A=24\ units^(2)+56\ units^(2)+36\ units^(2)=116\ units^(2)`