Answer:
[tex]\text{Area of the Land}=62906.91 ft^2[/tex]
Step-by-step explanation:
To determine the area of the land, we first determine the length of the base.
Since it is a isosceles trapezoid,
Length of the base =(228+2x)ft where x is the base of the triangle.
In the Right Triangle,
Perpendicular Height =209 ft
Hypotenuse =221.38 ft
Using Pythagoras Theorem:
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\221.38^2=209^2+x^2\\x^2=221.38^2-209^2\\x^2=5328.1044\\x=\sqrt{5328.1044} \\x=72.99\: ft[/tex]
Therefore, the length of the isosceles' trapezoid base
=228+2(72.99)=373.98ft
Area of a trapezoid
[tex]A=\frac{1}{2}(a+b)h\\$Where a and b are the parallel sides\\h=Perpendicular Height[/tex]
a=228ft, b=373.98ft, h=209ft
[tex]Area=\frac{1}{2}(228+373.98)209\\=\frac{1}{2}*601.98*209\\$Area of the Land=62906.91 ft^2[/tex]
