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[Solved] Polygons square

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ABCD is a square picture frame (see figure). EFGH is a square inscribed within ABCD as a space for a picture. The area of EFGH (for the picture) is equal to the area of the picture frame (the area of ABCD minus the area of EFGH). If AB=6, what is the length of EF?

 

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The area of the frame and the area of the picture sum to the total area of the image, which is \small 6^2,  or 36. Therefore, the area of the frame and the picture are each equal to half of 36, or 18. Since EFGH is a square, the length of EF is \small \sqrt{18},  or \small 3\sqrt{2}.

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