Find the area of an isosceles trapezoid with a lateral side 30 cm, a diagonal perpendicular

| August 7, 2021 | education

Find the area of an isosceles trapezoid with a lateral side 30 cm, a diagonal perpendicular to the lateral side and equal to 40 cm.

By condition, AC is perpendicular to CD, then triangle ACD is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse D.

AD ^ 2 = AC ^ 2 + CD ^ 2 = 40 ^ 2 + 30 ^ 2 = 1600 + 900 = 2500.

AD = 50 cm.

Determine the area of ​​the triangle ACD.

Sasd = AC * DC / 2 = 40 * 30/2 = 600 cm2.

The other side Sasd = AD * CK / 2.

SK = 2 * Sacd / AD = 2 * 600/50 = 24 cm.

From the right-angled triangle СDК, according to the Pythagorean theorem, we define the leg DК.

DK ^ 2 = CD ^ 2 – CK ^ 2 = 900 – 576 = 324.

DK = 18 cm.

Then НK = ВС = (АD – 2 * DК) = 50 – 36 = 14 cm.

Determine the area of ​​the trapezoid. Savsd = (BC + AD) * CK / 2 = (14 + 50) * 24/2 = 768 cm2.

Answer: The area of ​​the trapezoid is 768 cm2.



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