In an isosceles trapezoid, the bases are 2 and 8 and one of the angles between the side and the base is 45.

In an isosceles trapezoid, the bases are 2 and 8 and one of the angles between the side and the base is 45. Find the area of the trapezoid.

From the problem statement, we have an isosceles trapezoid ABCD

Let’s lower it from the top base to the bottom height and designate them as BE and CF, respectively. You can see that BC = EF = 2

Thus, we can say that the sum of the segments AE + FD = AD-EF = 8-2 = 6

Since the trapezoid is isosceles, we can say that AE = FD = 6/2 = 3

Consider a triangle ABE. We know that it is rectangular, since the height drops to the base at a right angle and its angle A is 45 degrees. That is, the angle B = 180-90-45 = 45

Based on this AE = BE = 3

That is, the height of the trapezoid is h = 3

Now let’s find the area from the formula:

S = ((a + b / 2) * h = ((8 + 2) / 2) * 3 = (10/2) * 3 = 5 * 3 = 15 cm sq.