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? The altitude of the trapezoid is __ feet.
(a+b)/2 * h = 8100
180/2 h = 8100
90h = 8100
h = 90
To find the altitude of the trapezoid, we can use the formula for the area of a trapezoid, which is given by:
Area = (1/2) * (base1 + base2) * height
In this case, we are given the sum of the bases (180 feet) and the area (8,100 square feet), and we are asked to find the height (altitude).
Let's substitute the given values into the formula and solve for the altitude:
8,100 = (1/2) * (base1 + base2) * height
Since we are given that the sum of the bases is 180 feet, we can rewrite the formula as:
8,100 = (1/2) * 180 * height
Now we can solve for the altitude by dividing both sides by (1/2) * 180:
8,100 / (1/2 * 180) = height
Simplifying the expression on the right-hand side, we have:
8,100 / 90 = height
Height = 90
Therefore, the altitude of the trapezoid (distance across the lot) is 90 feet.