In rectangle ABCD, E is a point on BC such that AD = 13, DE = 5, and EA = 12. Find the area of ABCD.
+23245 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.
