Find the area of an isosceles trapezoid if its diagonal is 2√13 and its height is 6 cm.

Let’s build the height CH and the diagonal AC of the trapezoid ABCD.

Since CH is the height, the triangle ACH is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg AH.

AH ^ 2 = AC ^ 2 – CH ^ 2 = 52 – 16.

AH = 4 cm.

Since the trapezoid is isosceles, and the CH height is drawn from the top of an obtuse angle to the larger base, it divides it into two segments, the length of the larger of which is equal to half the sum of the lengths of the bases of the trapezoid, which means it is equal to its midline.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = АН * СН = 4 * 6 = 24 cm2.

Answer: The area of the trapezoid is 24 cm2.