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In rectangle ABCD, E is a point on BC such that AD = 13, DE = 5, and EA = 12.  Find the area of ABCD.

 Jun 5, 2020
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By the Pythagorean Theorem, triangle(DEA) is a right triangle,

The area of triangle(DEA)  =  ½·5·12  =  30

 

Find the point F, on DA, that is directly across from point E.

 

1)  DCEF is a rectangle with DE dividing it into two congruent triangles. 

     Therefore, the area of triangle(DCE) = area of triangle(FED).

 

2)  ABEF is a rectaongle with AE dividing it into two contruent triangles.

     Therefore, the area of triangle(BAE) = area of triangle(FEA).

 

3)  Since the area of triangle(DEF) + area of triangle(AEF) = 30,

      the area of triangle(DCE) + area of triangle(ABE) = 30,

      and the total area of the rectangle is 60.

 Jun 5, 2020

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