The smaller side of a rectangular trapezoid is 9 cm and an acute angle of 45 degrees. find the area of the trapezoid.

To solve this problem, we must understand that, in fact, a straight trapezoid consists of a rectangle and a right-angled triangle. Let’s start with a triangle in this trapezoid, we know that it has angles of 90 and 45 degrees. From this it follows that the third angle is (180-90-45) = 45. From the properties of the triangle, we can assume that this triangle is isosceles, which means that the size of the large side will be equal to the height of the trapezoid (H) (from the properties of the triangle). So the area of ​​this trapezoid will be equal to:
S = ((4 + H) +4) H.
S = 4H + H ^ 2 + 4H
S = H ^ 2 + 8H.
Answer: S = H ^ 2 + 8H is the area of ​​this trapezoid.