The bisector of angle A of rectangle ABCD intersects side BC at point E so that BE = 4.5 cm

The bisector of angle A of rectangle ABCD intersects side BC at point E so that BE = 4.5 cm, CE = 5.5 cm. Find the area of the rectangle.

AE is the bisector of angle A, which means <BAE = <AEB = 90: 2 = 45 °,

The angles at the base are equal, so the triangle ABE is isosceles, that is, AB = BE = 4.5 cm;

The area of a rectangle is equal to the product of its sides:

S = AB * BC;

BC = BE + EC = 4.5 + 5.5 = 10 (cm);

S = 4.5 * 10 = 45 (cm²).