Find the larger base of the trapezoid if its area is 240cm ^ 2, height is 12cm, and the smaller base is 15cm.

Because the area of the trapezoid is calculated by the formula S = 1/2 * (a + b) * h, where a and b are the bases and h is the height, you can find the half-sum of the bases as the ratio of area to height:

1/2 * (a + b) = 240/12,

1/2 * (a + b) = 20 (cm).

If we know that a = 15 cm, we find what the second base is equal to:

1/2 * (15 + b) = 20,

15 + b = 20 * 2,

15 + b = 40,

b = 40 – 15,

b = 25 (cm).

Answer: the base of the trapezoid, which is larger in length, is 25 cm.