An isosceles trapezoid has bases of 4 and 10. if the base angle is 45°, find the area.

Extend the ends of the smaller base, 4, down to the longer base to create a rectangle and 2 triangles. The base of the triangles is 3. The angle adjacent to this side is 45 degrees. This means that the height is also three. The area of the trapezoid is given by the equation,
                                    A = (b1 + b2) / 2   x h
Substituting, 
                                   A = (4 + 10) / 2     x 3 = 21 
Thus, the area of the trapezoid is 21 squared units.