In the rhombus ABCD, the height of the BC is drawn equal to 5√2, find the area of the rhombus if the angle ABC is 45.

In a rhombus, the opposite sides are parallel, and since AK is a continuation of AD, BC is parallel to DK.

Then the angle ABC = BAK = 450, as the angles lying crosswise at the intersection of parallel straight lines BC and DK secant AB.

The AВK triangle is rectangular and isosceles, since one of its angles is 45.

Then KA = ВK = 5 * √2 cm.

AB ^ 2 = ВK ^ 2 + AK ^ 2 = 50 + 50 = 100.

AB BC = AD = CD = 10 cm.

Determine the area of the rhombus.

Savsd = AD * ВK = 10 * 5 * √2 = 50 * √2 cm2.

Answer: The area of the rhombus is 50 * √2 cm2.