The sides of the green roof are rectangles. Use the Pythagorean Theorem to calculate the width of each side of the roof.
$1020
Practice makes perfect
We want to find how much it costs to cover both sides of a roof with plants. To do so, we will need to calculate the area of the roof. Let's look at the given diagram.
Each side of the roof is a rectangle. We can calculate the areas using the formula for the area of a rectangle.
A=l w
In the formula, l is the length and w is the width of the rectangle. We know that each side of the roof is 40 feet long. This means that to calculate the areas, we only need to find the widths. Let's draw the roof from another angle.
We can see that the height of the roof divides the front of the house into two right triangles. Notice that the hypotenuse of each triangle is the width of the corresponding roof side. We will use the Pythagorean Theorem to calculate the width of the right side of the roof.
a^2+b^2=c^2
In the formula, a and b are the legs and c is the hypotenuse of a right triangle. Let's identify a, b, and c on the diagram.
Here we have that a= 8 feet and b= 15 feet. Let's substitute these values into the formula.
The right side of the roof has a width of 17 feet. Because both triangles have the same leg measurements, the hypotenuses will also be the same length. This means that the left side of the roof has a width of 17 feet as well! We can add this information to the diagram.
The roof has a length l of 40 feet and a width w of 17 feet. Let's find the area of one side of the roof by substituting these values into the formula for the area of a rectangle.
The area of one side of the roof is 680 square feet. We know that both sides of the roof have the same measurements so the area of the roof is twice the area of one side.
2 * 680= 1360
The area of the roof is 1360 square feet. We know that 1 square foot of plants costs $0.75. To find how much it costs to cover the roof, we will multiply the area of the roof by $0.75. Let's do it!
1360 * $0.75 = $1020
The cost of covering both sides of the roof is $1020.
