The area of a rectangular trapezoid is 120 cm2 and its height is 8 cm

The area of a rectangular trapezoid is 120 cm2 and its height is 8 cm, find all sides of the trapezoid if one of the bases is 6 cm larger than the other.

Let the smaller base be equal to X cm, then the larger base, by condition, is equal to (X + 6) cm.

Then Savsd = (BC + AD) * CH / 2 = (X + X + 6) * 8/2 = 120.

4 * X + 24 = 120.

4 * X = 96.

X = BC = 96/4 = 24 cm.

Then AD = 24 + 6 = 30 cm.

Segment DH = AD – AH = AD – BC = 30 – 24 = 6 cm.

In a right-angled triangle СDН, according to the Pythagorean theorem, we determine the length of the hypotenuse СD.

CD ^ 2 = CH ^ 2 + DH ^ 2 = 64 + 36 = 100.

СD = 10 cm.

Side AB = CH = 8 cm.

Answer: The sides of the trapezoid are 8 cm, 24 cm, 10 cm, 30 cm.