the high of a trapezoid is 10ft the upper base is 6ft shorter then the lower base if the area of the trapezoid is 50 square ft how long is the upper and lower base?

To find the lengths of the upper and lower bases of the trapezoid, we can use the formula for the area of a trapezoid:

Area = (1/2) * (upper base + lower base) * height

Given that the height (h) is 10 ft and the area (A) is 50 square ft, we can substitute these values into the formula:

50 = (1/2) * (upper base + lower base) * 10

Let's simplify the equation by removing the fraction:

100 = (upper base + lower base) * 10

Now, let's solve for the difference between the upper and lower bases.

Let's assume the lower base is x, so the upper base is (x - 6) since it's 6 ft shorter.

Using this assumption, we can rewrite the equation as:

100 = (x + (x - 6)) * 10

Simplifying further:

100 = (2x - 6) * 10

Now, we can solve for x:

10(2x - 6) = 100

20x - 60 = 100

20x = 160

x = 8

Now that we have found the value of x, which is the length of the lower base, we can substitute it back into our assumption to find the length of the upper base:

Upper base = 8 - 6 = 2 ft

Therefore, the upper base is 2 ft and the lower base is 8 ft.