Question

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

Answer 1

Answer:

270 ft²

Step-by-step explanation:

METHOD 1:

Look at the picture

We can divide a given polygon into three rectangles:

$21ft\ \times\ 10ft,\ 4ft\ \times\ 6ft,\ 6ft\ \times\ 6ft$

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):

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