The bisector of angle A of rectangle ABCD intersects side BC at point BE = 4.5cm, CE = 5.5cm

The bisector of angle A of rectangle ABCD intersects side BC at point BE = 4.5cm, CE = 5.5cm. What is the area of the rectangle?

Since ABCD is a rectangle, the bisector AM divides the right angle in half.

Then the angle BAM = BAD / 2 = 90/2 = 45.

The ABM triangle is rectangular, in which one of the acute angles is 450, then this triangle is also isosceles, which means: AB = BM = 4.5 cm.

Side length BC = BM + CM = 4.5 + 5.5 = 10 cm.

Then the area of the rectangle is:

Savsd = AB * BC = 4.5 * 10 = 45 cm2.

Answer: The area of the rectangle is 45 cm2.