The bisector of one of the corners of the rectangle divides one of its sides into two segments 5 cm

The bisector of one of the corners of the rectangle divides one of its sides into two segments 5 cm and 6 cm long. Find the square.

1. By the condition of the problem, it is known that the side of the rectangle is divided by the bisector of the angle into segments of 5 cm and 6 cm.

2. The bisector cut off a right-angled triangle from the rectangle, one angle of which is 90 °: 2 = 45 °.

Let’s define the second acute angle: 180 ° – 45 ° = 45 °, that is, the triangle is also isosceles, and then the length of both legs is 5 cm, which means the width of the rectangle.

The length of the rectangle is 5 cm + 6 cm = 11 cm.

Let’s calculate its area:

5 cm * 11 cm = 55 cm².

Answer: The required area is 55 cm².