If the ratio of the base for two similar trapezoids is 24:59, and the area of the smaller trapezoid is 564 m^2, what is the area of the bigger trapezoid?
Let the base of the smaller trapezoid be 24x and the base of the larger trapezoid be 59x, where x is a constant.
Since the trapezoids are similar, the ratio of their areas is equal to the square of the ratio of their bases. Therefore:
Area of smaller trapezoid / Area of larger trapezoid = (24x)^2 / (59x)^2
564 / Area of larger trapezoid = (24/59)^2
Area of larger trapezoid = 564 * (59/24)^2
Area of larger trapezoid = 564 * (3481/576)
Area of larger trapezoid = 3408.25
Therefore, the area of the larger trapezoid is 3408.25 m^2.