A lot is in the shape of a trapezoid. The sum of the bases is 180 feet. If the area of the lot is 8,100 square feet, what is the distance across the lot, i.e., the altitude of the figure?

http://www.mathopenref.com/trapezoidarea.html

a = h(b1 + b2)/2
8100 = 90h
8100/90 = h
90 = h

Find the area of the following circle.

r = 9 yd.

To find the distance across the lot, we need to determine the altitude of the trapezoid.

Let's denote the length of the shorter base as "a" and the length of the longer base as "b". We are given that the sum of the bases is 180 feet, so we can write the equation:

a + b = 180

The formula to calculate the area of a trapezoid is (1/2) * altitude * (sum of the bases). In this case, the area of the lot is given as 8,100 square feet. So we have:

(1/2) * altitude * (a + b) = 8,100

Substituting the value of (a + b) from the first equation into the second equation, we get:

(1/2) * altitude * 180 = 8,100

Multiplying both sides by 2 and dividing by 180, we obtain:

altitude = 8,100 * 2 / 180

Simplifying further:

altitude = 90 feet

Therefore, the distance across the lot, i.e., the altitude of the trapezoid, is 90 feet.