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jcherry99
Comment
In a 45 - 45 - 90 triangle the two smaller sides are =. So when you use 
a^2 + b^2 = c^2, you need a and b both to find the area.

So call both of them = b^2.

Equation and solution
a^2 + b^2 = c^2
b^2 + b^2 = c^2
2b^2 = c^2
c = 24
b = ???

2 b^2 = 24^2
2 b^2 = 576 Divide by 2
b^2 = 288 I'm going to leave this as it is for the moment. You'll see what in a second.

Area of a triangle
Area of a triangle = 1/2 h * b
But the height and base are the 2 smaller equal sides of a 45_45_90 triangle
so h = b
base = b 

Area of a triangle = 1/2 b^2 The equalities above tell you that. h and b of the triangle are equal.

Area = 1/2 288 feet^2
Area = 144 feet^2

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