E does not belong to plane ABCD, ED = 25, BD = 7, ABCD is a rectangle, BE is perpendicular to AB

E does not belong to plane ABCD, ED = 25, BD = 7, ABCD is a rectangle, BE is perpendicular to AB, AE is perpendicular to AD Find: area BED Prove: AD is perpendicular to BE

Since, by condition, BE is perpendicular to AB, then BE is perpendicular to the plane of the rectangle ABCD. Then BE is perpendicular to BC. AD is parallel to BC, and therefore BE is perpendicular to AD, which was required to be proved.

The BED triangle is rectangular, then, according to the Pythagorean theorem, BE ^ 2 = DE ^ 2 – BD ^ 2 = 625 – 49 = 576.

BE = 24 cm.

Determine the area of the triangle BED. Swed = BE * BD / 2 = 24 * 7/2 = 84 cm2.

Answer: The area of the BED triangle is 84 cm2.