One of the corners of a rectangular trapezoid = 45 degrees. Calculate the area of the trapezoid if its bases are 4 cm and 8 cm.

From the top of the trapezoid, we will construct the height CH.

Since the trapezoid is rectangular, and CH is height, then the quadrilateral ABCH is a rectangle, then AH = BC = 4 cm, and DH = AD – AH = 8 – 4 = 4 cm.

The CHD triangle is rectangular, in which one of the acute angles is 45, then the CHD triangle is isosceles, CH = DH = 4 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (4 + 8) * 4/2 = 24 cm2.

Answer: The area of the trapezoid is 24 cm2.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.