Question

Can someone please help me find the area of this polygon, thank you!

Answer 1

270 ft²

Explanation:

METHOD 1:

Look at the picture

We can divide a given polygon into three rectangles:

`21ft\ *\ 10ft,\ 4ft\ *\ 6ft,\ 6ft\ *\ 6ft`

The formula of an area of a rectangle l × w :

`A=l\cdot w`

Calculate the area of ​​each of the rectangles:

`A_1=(21)(10)=210\ ft^2\\\\A_2=(4)(6)=24\ ft^2\\\\A_3=(6)(6)=36\ ft^2`

The area of the given polygon:

`A=A_1+A_2+A_3\\\\A=210+24+36=270\ ft^2`

METHOD 2:

Look at the second picture.

We subtract the field of the smaller rectangle (11ft × 6ft) from the field of the large rectangle (21ft × 16ft):

`A_S=(11)(6)=66\ ft^2\\\\A_L=(21)(16)=336\ ft^2\\\\A=A_L-A_S\to A=336-66=270\ ft^2`