Answer:
The price is $1.6 per square foot of the land
Step-by-step explanation:
step 1
Find the area of the plot of land
we know that
The area of the plot of land is equal to the area of trapezoid 1 plus the area of trapezoid 2
see the attached figure to better understand the problem
Remember that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}[b1+b2]h[/tex]
Find the area of trapezoid 1
we have
[tex]b1=125\ ft[/tex]
[tex]b2=265\ ft[/tex]
[tex]h=260-150=110\ ft[/tex]
substitute
[tex]A1=\frac{1}{2}[125+265](110)[/tex]
[tex]A1=21,450\ ft^{2}[/tex]
Find the area of trapezoid 2
we have
[tex]b1=150\ ft[/tex]
[tex]b2=265\ ft[/tex]
[tex]h=150\ ft[/tex]
substitute
[tex]A2=\frac{1}{2}[150+265](150)[/tex]
[tex]A2=31,125\ ft^{2}[/tex]
The area total of the land is
[tex]A=A1+A2[/tex]
[tex]A=21,450+31,125=52,575\ ft^{2}[/tex]
step 2
Find the price per square foot of the land
Divide the total cost by the total area
[tex]\frac{84,120}{52,575}=1.6\frac{\$}{ft^{2}}[/tex]
