MHB What is the Surface Area of a Square with Given Points and Side Lengths?

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The discussion focuses on calculating the surface area of square ABCD using given points E and F, with specific angles and lengths. The angles ∢AEF and ∢EFC are both 90 degrees, while the lengths AE, CF, and EF are 2, 6, and 6, respectively. The diagonal length |AC| is provided as 10, which is crucial for determining the side length of the square. By applying the Pythagorean theorem, the side length of square ABCD can be derived. Ultimately, the surface area can be calculated once the side length is established.
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Let E, F be such points inside the ABCD square that | ∢AEF | = | ∢EFC | = 90∘ and | AE | = 2, | CF | = 6 and | EF | = 6. Calculate the surface of ABCD.
 
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$|AC| = 10$ ... see what you can do with that piece of information
 

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