1 Answer

Trinition · Answer 1 · 2021-10-19T07:40:46+0000

Answer:

270 ft²

Explanation:

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:

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

Look at the second picture.

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

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