Find the area of an isosceles trapezoid if its diagonal is 2 and the height is 8.

Let’s build the height BH of the trapezoid ABCD.

In a right-angled triangle BDH, according to the Pythagorean theorem, we determine the length of the leg DH.

DH ^ 2 = BD ^ 2 – BH ^ 2 = 68 – 64 = 4.

DН = 2 cm.

In an isosceles trapezoid, the height, drawn to the larger base, divides it into two segments, the length of the larger of which is equal to half the sum of the lengths of its bases, that is, equal to the midline of the trapezoid.

Then Savsd = DH * BH = 2 * 8 = 16 cm2.

Answer: The area of the trapezoid is 16 cm2.