The angles at the base of the trapezoid are 90 and 45. One base is twice the size of the other

The angles at the base of the trapezoid are 90 and 45. One base is twice the size of the other and is equal to 24 cm. Find the smaller side.

Let the larger base of the trapezoid be 24 cm, and the smaller base equal to 24: 2 = 12 cm. The fact that the angle at the base is 90 degrees indicates that the trapezoid is rectangular, and the smaller side is equal to the height of the trapezoid.

Dropping the height from the second point of the top base to the bottom base, we get a right-angled triangle with an angle of 45 degrees. and legs equal to 12 cm and 12 cm.

This means that the smaller side, equal to the height of the trapezoid, is equal to the leg of a right-angled triangle, and 12 cm.

Answer: 12 cm.