Answer:
270 ft²
Step-by-step explanation:
METHOD 1:
Look at the picture
We can divide a given polygon into three rectangles:
[tex]21ft\ \times\ 10ft,\ 4ft\ \times\ 6ft,\ 6ft\ \times\ 6ft[/tex]
The formula of an area of a rectangle l × w :
[tex]A=l\cdot w[/tex]
Calculate the area of each of the rectangles:
[tex]A_1=(21)(10)=210\ ft^2\\\\A_2=(4)(6)=24\ ft^2\\\\A_3=(6)(6)=36\ ft^2[/tex]
The area of the given polygon:
[tex]A=A_1+A_2+A_3\\\\A=210+24+36=270\ ft^2[/tex]
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):
[tex]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[/tex]
