The smaller side of a rectangular trapezoid is 10 cm, and the acute angle is 45 degrees. Find the area

The smaller side of a rectangular trapezoid is 10 cm, and the acute angle is 45 degrees. Find the area of the trapezoid if you can fit a circle into it.

1) draw the height from, in the trapezoid of the avsd.
2) co = ab = 10
3) consider the triangle sod: according to trigonometric formulas сd = 10 * 2 / √2 = 10√2.
4) if a circle can be inscribed in a trapezoid, then sun + hell = cd + ab = 10 + 10√2.
5) the area of the trapezoid = (sun + hell) / 2 = (10 + 10√2) / 2 = 5 + 5√2.