The cost for paint to cover the exterior of the four sides of a shed was $80. A can of paint costs $20 and will cover 24 square feet. The shed consists of four sides, each shaped like a trapezoid. They each have one base of 5 feet and one base of 7 feet. What is the altitude of each trapezoid?
wrong again!!!!
number of cans of paint = 80/20 = 4
so we have 4 cans for 4 equal sides
so, 1 can per side , or 24 square ft per side
(1/2)(5+7)(h) = 24
12h = 48
h = 4 <----- altitude
To find the altitude of each trapezoid, we need to know the area of each side and then use the formula for the area of a trapezoid.
Let's find the area of one side first.
The formula for the area of a trapezoid is A = (b1 + b2) * h / 2, where b1 and b2 are the lengths of the bases, and h is the altitude.
Given that one base is 5 feet and the other base is 7 feet, we can plug these values into the formula:
A = (5 + 7) * h / 2
To find the altitude, h, we need to rearrange the formula:
2A = (5 + 7) * h
2A = 12h
h = 2A / 12
Now, let's find the area of one side of the shed.
We know that a can of paint covers 24 square feet, and the cost to paint all four sides is $80. Since the cost is directly proportional to the area, we can set up a proportion:
24 square feet = $20
x square feet = $80
x = (24 * $80) / $20
x = 96 square feet
Now we have the area of one side of the shed, which is 96 square feet. Plugging this value into the equation for the altitude:
h = 2A / 12
h = 2 * 96 / 12
h = 16 feet
Therefore, the altitude of each trapezoid is 16 feet.
To find the altitude of each trapezoid, we need to determine the total area of the four sides of the shed and then divide it by the sum of the lengths of the bases.
Let's start by calculating the area of each trapezoid. The formula to find the area of a trapezoid is:
Area = (a + b) * h / 2,
where a and b are the lengths of the bases, and h is the altitude.
For each trapezoid, the base lengths are 5 feet and 7 feet. Let's assume the altitude for each trapezoid is h feet. The total area of all four trapezoids is given as 80 square feet, so we can write the equation:
[(5 + 7) * h / 2] * 4 = 80.
Simplifying the equation:
(12 * h / 2) * 4 = 80,
6 * h * 4 = 80,
24h = 80,
h = 80 / 24,
h = 3.33 (rounded to two decimal places).
Therefore, the altitude of each trapezoid is approximately 3.33 feet.
The altitude of each trapezoid is 8 feet.
To calculate this, we need to find the area of each trapezoid. The area of a trapezoid is (base1 + base2) / 2 * altitude.
So, we can set up the equation as follows:
(5 + 7) / 2 * altitude = 24
12 * altitude = 24
Altitude = 24 / 12
Altitude = 8 feet