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