The angle at the base of an isosceles trapezoid is 45 degrees, the lateral side is 8 cm

The angle at the base of an isosceles trapezoid is 45 degrees, the lateral side is 8 cm, the smaller base is 10 cm, which is equal to the middle line of the trapezoid.

Let’s mentally draw the height to the larger base of our trapezoid.

We will get a right-angled triangle with one of the sharp corners of which, according to the condition of the problem, an angle of 45 °. Let’s define the second acute angle:

90 – 45 = 45.

That is, the triangle is isosceles.

Let’s determine how long the leg will be in it, knowing that the hypotenuse is 8 cm:

8 * √2 / 2 = 4√2.

Then the length of the second base will be equal to:

10 + 2 * 4√2 = 10 + 8√2.

Determine the length of the midline:

(10 + 10 + 8√2): 2 = 10 + 4√2.

Answer: 10 + 4√2 cm.