The bases of an isosceles trapezoid are 11 and 23 dm, and the lateral side is 10 dm. Calculate the height of the trapezoid.

To solve the problem, we divide the trapezoid into 2 triangles and a rectangle, draw two heights and get that the base is 11 dm.

Consider a triangle, it has two heights. One height – 10 dm. The second can be found:
(23 – 11) / 2 = 6. Since the trapezoid is isosceles, the triangles are the same.

Then we find the height according to the Pythagorean theorem:
h ^ 2 + 6 ^ 2 = 10 ^ 2;
h ^ 2 = 100 – 36;
h ^ 2 = 64;
h = 8.

Answer: 8.