In trapezoid ABCD angles A and B = 90 degrees angle D = 45 degrees find the middle line

In trapezoid ABCD angles A and B = 90 degrees angle D = 45 degrees find the middle line of the trapezoid if AD = 14, AB = 6.

Let’s lower the height from the top C – CH.

Consider a triangle СНD: angle Н = 90, angle D = 45.

Find angle C using the fact that the sum of the angles of the triangle is 180: 180 – 90 – 45 = 45.

Hence, since С = D, then СН = НD = BA (according to the condition of the problem) = 6.

Now we find BC: BC = AH = AD – HD = 14 – 6 = 8.

For the formula of the middle line of the trapezoid: BC + AD = 22; 22/2 = 11.

Answer: 11.