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?
since the area is h(a+b)/2,
h (180/2) = 8100
90h = 8100
h = 90
To find the altitude of the trapezoid, we need to use the formula for the area of a trapezoid:
Area = (1/2) * (base1 + base2) * height
In this case, the area is given as 8,100 square feet and the sum of the bases is given as 180 feet. Let's use these values to find the altitude.
First, let's rearrange the formula to solve for the height:
Area = (1/2) * (base1 + base2) * height
8,100 = (1/2) * 180 * height
Now, let's simplify the equation:
8,100 = 90 * height
Divide both sides by 90:
height = 8,100 / 90
height = 90 feet
Therefore, the altitude of the trapezoid, or the distance across the lot, is 90 feet.