The side of the parallelogram is equal to one of its diagonals and is 8. The length of the second diagonal

| January 6, 2021 | education

The side of the parallelogram is equal to one of its diagonals and is 8. The length of the second diagonal of the parallelogram is 8 root of 2 find the area of the parallelogram.

Consider a parallelogram ABCD with side AB = CD = 8 cm and diagonal BE = AB = 8 cm. Side AD = BC = 8 * √2.
Triangle ABD is equilateral on two sides, then the height BE drawn to side AD divides it in half.
AE = AD / 2 = (8 * √2) / 2 = 4 * √2.
Consider a right-angled triangle ABE and find, by the Pythagorean theorem, leg BE, which is the height of the parallelogram.
BE ^ 2 = AB ^ 2 – AE ^ 2 = 8 ^ 2 – (4 * √2) ^ 2 = 64 – (16 * 2) = 32.
BE = √32 = (√16 * 2) = 4 * √2.
Find the area of the parallelogram.
S = AD * BE = (8 * √2) * (4 * √2) = 32 * 2 = 64 cm2.
Answer: The area of the parallelogram is 64 cm2.



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