The cost for paint to cover the exterior of the four sides of a shed was $40. A can of paint costs $10 and will cover 33 square feet. the shed has 4 sides, each shaped like a trapezoid. they each have one base of 5 feet and one base of 6 feet. what is the altitude of each trapezoid?
To find the altitude of each trapezoid, we need to calculate the total area that needs to be painted and then divide it by the base length to get the altitude.
First, let's find the area of one trapezoid. The formula for the area of a trapezoid is:
Area = (1/2) * (sum of the bases) * altitude
Given that one base is 5 feet (b1 = 5 ft) and the other base is 6 feet (b2 = 6 ft), we can set up the equation:
Area = (1/2) * (b1 + b2) * altitude
Since there are four sides on the shed, the total area to be painted is 4 times the area of one trapezoid. Therefore:
Total Area = 4 * Area
Now, let's calculate the total area:
Total Area = 4 * (1/2) * (5 + 6) * altitude
Total Area = 4 * (1/2) * 11 * altitude
Total Area = 2 * 11 * altitude
Total Area = 22 * altitude
We are given that the cost to paint the shed is $40, and we know that a can of paint, costing $10, covers 33 square feet. So, if the total area is 22 * altitude, we can set up the following equation:
Total Area / Coverage of one can = Number of cans
22 * altitude / 33 = Number of cans
Now, we can solve for the number of cans:
40 / 10 = (22 * altitude) / 33
4 = (22 * altitude) / 33
4 * 33 = 22 * altitude
132 = 22 * altitude
altitude = 132 / 22
altitude = 6 feet
Therefore, the altitude of each trapezoid (or the height of each side) is 6 feet.