In parallelogram ABCD, BD is perpendicular to AB, BE is perpendicular to AD, BE = 6cm, AE = 3cm. Find the area of the parallelogram.
By condition DB is perpendicular to the lateral side AB, then triangle ABD is rectangular, and its height BE is drawn to the hypotenuse from a right angle.
Then BE = √ (AE * DE).
We square both sides of the equality and express DE.
BE ^ 2 = AE * DE.
DE = BE ^ 2 / AE = 36/3 = 12 cm.
Then the length of the base is AD = AE + DE = 3 + 12 = 15 cm.
Determine the area of the parallelogram.
Savsd = AD * BE = 15 * 6 = 90 cm2.
Answer: The area of the parallelogram is 90 cm2.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.