In an isosceles trapezoid, the side, height and diagonal are equal to √117, 9, 15. Find the area of the trapezoid

univerkov | April 18, 2021 | education

The height of CH forms a right-angled triangle CDH, from which, according to the Pythagorean theorem, we determine the leg DH.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 117 – 81 = 36.

DН = 6 cm.

From the right-angled triangle ACN, we determine the length of the leg AH.

AH ^ 2 = AC ^ 2 – CH ^ 2 = 225 – 81 = 144.

AH = 12 cm.

Then AD = AN + DN = 12 + 6 = 18 cm.

Since the trapezoid is isosceles, then BC = AD – 2 * DN = 18 – 2 * 6 = 6 cm.

Determine the area of the trapezoid.

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

Answer: The area of the trapezoid is 108 cm2.

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