To find the height of a trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) * (base1 + base2) * height
Given that the area is 100 in sq, base1 is 12, and base2 is 13, we can substitute these values into the formula:
100 = (1/2) * (12 + 13) * height
Now we can simplify and solve for the height:
100 = (1/2) * 25 * height
Multiplying both sides by 2 to eliminate the fraction:
200 = 25 * height
Dividing both sides by 25:
height = 200 / 25
height = 8
Therefore, the height of the trapezoid is 8 inches.