The sides of the rectangular trapezoid ABCD are 10cm, 8cm. Its larger base AD = 18cm.

The sides of the rectangular trapezoid ABCD are 10cm, 8cm. Its larger base AD = 18cm. Calculate the length of the smaller base of the trapezoid and the length of its midline.

Obviously, in this trapezoid, the side AB, perpendicular to the bases, is 8 cm, and the oblique side CD is 10 cm.

The length of the larger base AD is equal to the sum of the lengths of the smaller base BC and the projection of the oblique lateral side onto the larger base. The height CK of this trapezoid is equal to the smaller lateral side AB.

Consider a right-angled triangle formed by an oblique lateral side CD, its projection KD onto a larger base, and the height of the trapezoid CK. According to the Pythagorean theorem, the square of the projection can be found as the difference between the squares of the side and the height:

KD ^ 2 = CD ^ 2 – CK ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36 = 62;

KD = 6 cm.

We find the length of the smaller base as the difference between the lengths of the larger base and the projection of the lateral side:

BC = 18 – 6 = 12 cm.

The middle line is equal to half the sum of the lengths of the bases:

m = (BC + AD) / 2 = (12 + 18) / 2 = 30/2 = 15 cm.