The difference between the bases of the trapezoid is 6m, the height is 22m, the area is 594. find the bases of the trapezoid.

It is known from the condition that the difference between the bases of the trapezoid is 6 meters.

We carry the variable x – denoting with its help the length of the smaller side, then the length of the larger side is equal to (x + 6) meters.

It is also known that the height is 22 meters, and the area is 594 m ^ 2.

We apply the formula for the area of a trapezoid to calculate the lengths of the bases of a trapezoid:

S = (a + b) / 2 * h

(x + x + 6) / 2 * 22 = 594;

11 (2x + 6) = 594;

We solve the equation:

2x + 6 = 54;

2x = 48;

x = 24 meters smaller base and 24 + 6 = 30 meters larger base.