Question

3. A recent tornado in a small town in Southwest New York destroyed and damaged

multiple plots of land. The insurance company has been surveying these plots of land to
write their report on the damage assessment. One plot of land is the shape of an
isosceles trapezoid, and the insurance must determine the area of the land.

Answer 1

`\text{Area of the Land}=62906.91 ft^2`

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:

`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=√(5328.1044) \\x=72.99\: ft`

Therefore, the length of the isosceles' trapezoid base

=228+2(72.99)=373.98ft

Area of a trapezoid

`A=(1)/(2)(a+b)h\\$Where a and b are the parallel sides\\h=Perpendicular Height`

a=228ft, b=373.98ft, h=209ft

`Area=(1)/(2)(228+373.98)209\\=(1)/(2)*601.98*209\\$Area of the Land=62906.91 ft^2`