Question 1102095
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First let's draw a picture of what this could look like
<img src = "https://i.imgur.com/GGF807q.png">
The longer base is horizontally placed along the bottom, which is the distance from point A to point B. So AB = 18 feet.


The nonparallel sides, AD and BC are both 11 feet long. So AD = 11 and BC = 11. 
We don't know the length of CD, which is the length of the other parallel side. 
We'll need this to find the area of the trapezoid. For now, let's call it x. So CD = x.


To help find CD, let's drop a perpendicular line straight down from points C and D like shown below
<img src = "https://i.imgur.com/XwQ0mra.png">
Those perpendicular lines, the dashed vertical ones, drop to points E and F as shown in the figure. 
The distance from D to E is some unknown height h.


The distance from A to E is unknown. We'll call it y. So AE = y. 
Because we have an isosceles trapezoid, we have symmetry along the vertical center line. 
This means FB = y as well. The length of EF is equal to the length of CD. This means EF = x. 


Overall, AE+EF+FB = AB translating to y+x+y = 18 or x+2y = 18. Solve for x to get x = -2y+18. 
If we knew the value of y, then we can find x.


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To find the value of y, we'll use trigonometry. We'll use the cosine rule


cos(angle) = adjacent/hypotenuse
cos(80) = AE/AD
cos(80) = y/11
11*cos(80) = y
y = 11*cos(80) <font color=blue>this is the exact length of AE and FB</font>
y = 1.910130 <font color=blue>this is the approximate length of AE and FB (rounded to 6 decimal places)</font>


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We now know the approximate value of y so that makes x to be roughly...
x = -2*y+18
x = -2*1.910130+18
x = 14.17974


So the other parallel side, CD, is roughly 14.17974 feet long


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We're almost at the finish line. We need to find the height h. 
We'll use trig again, but this time the sine rule


sin(angle) = opposite/hypotenuse
sin(80) = h/11
h = 11*sin(80)
h = 10.832885


The height of this trapezoid is roughly 10.832885 feet.

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In summary so far, we found


x = 14.17974
h = 10.832885


Which allows us to finally find the area of this trapezoid


Use this area formula
Area of Trapezoid = h*(b1+b2)/2
where,
h = height
b1 & b2 = the parallel bases


So,
Area of Trapezoid = h*(b1+b2)/2
Area of Trapezoid = 10.832885*(14.17974+18)/2
Area of Trapezoid = 174.29971137495


Which is approximate. Due to the approximate nature of the answer, there is likely to be rounding error. 
Use more decimal digits in the values of x and h to reduce the rounding error. 


Side Note: the units for the answer are "square feet".
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