# In an isosceles trapezoid, the side, height and diagonal are equal to the root of 117,9,15, respectively.

In an isosceles trapezoid, the side, height and diagonal are equal to the root of 117,9,15, respectively. find the area of the trapezoid

From the right-angled triangle ABK, according to the Pythagorean theorem, we determine the length of the leg AK.

AK ^ 2 = AB ^ 2 – BK ^ 2 = 117 – 81 = 36.

AK = 6 cm.

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

DK ^ 2 = BD ^ 2 – BK ^ 2 = 225 – 81 = 144.

DK = 12 cm.

Since the trapezoid is isosceles, then DH = AK = 6 cm.

Base length AD = AK + DK = 6 + 12 = 18 cm.

KN = DK – AK = 12 – 6 = 6 cm, then BC = KН = 6 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СK / 2 = (6 + 18) * 9/2 = 108 cm2.

Answer: The area of the trapezoid is 108 cm2. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.