Question
Lizzie and her wife need to paint the walls of their bedroom. The room is 12 feet by 14 feet, and it has a ceiling that is 10 feet high. What is the area that they need to paint?
To find the area that they need to paint, we need to calculate the total surface area of the walls in the bedroom.
The bedroom has four walls - two shorter walls and two longer walls.
The area of each shorter wall can be calculated by multiplying the height (10 feet) by the width (12 feet):
Shorter wall area = 10 feet * 12 feet = 120 square feet
The area of each longer wall can be calculated by multiplying the height (10 feet) by the length (14 feet):
Longer wall area = 10 feet * 14 feet = 140 square feet
Since there are two shorter walls and two longer walls, the total area of all four walls is:
Total wall area = 2 * (Shorter wall area) + 2 * (Longer wall area)
Total wall area = 2 * (120 square feet) + 2 * (140 square feet)
Total wall area = 240 square feet + 280 square feet
Total wall area = 520 square feet
Therefore, Lizzie and her wife need to paint an area of 520 square feet.
Are you sure?
Apologies for the miscalculation. Let's recalculate the area that needs to be painted.
The bedroom has four walls - two shorter walls and two longer walls.
The area of each shorter wall can be calculated by multiplying the height (10 feet) by the width (12 feet):
Shorter wall area = 10 feet * 12 feet = 120 square feet
The area of each longer wall can be calculated by multiplying the height (10 feet) by the length (14 feet):
Longer wall area = 10 feet * 14 feet = 140 square feet
Since there are two shorter walls and two longer walls, the total area of all four walls is:
Total wall area = 2 * (Shorter wall area) + 2 * (Longer wall area)
Total wall area = 2 * (120 square feet) + 2 * (140 square feet)
Total wall area = 240 square feet + 280 square feet
Total wall area = 520 square feet
Therefore, Lizzie and her wife need to paint an area of 520 square feet. My previous response was correct.
Thank you so much?
You're welcome! If you have any more questions, feel free to ask. Happy painting!
Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.
To find the surface area of a rectangular pyramid, we need to calculate the areas of the individual faces and then add them up.
The formula for the surface area of a rectangular pyramid is:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Given that the length (l) of the rectangular base is 15 m, the width (w) is 12 m, and the height (h) is 10 m, we can calculate the surface area.
The base of the pyramid is a rectangle, so the base area is:
Base Area = length * width = 15 m * 12 m = 180 m^2
To calculate the slant height, we'll use the Pythagorean theorem. The slant height (s) can be calculated as:
s = sqrt(l^2 + w^2 + h^2)
s = sqrt(15^2 + 12^2 + 10^2)
s = sqrt(225 + 144 + 100)
s = sqrt(469)
s ≈ 21.63 m
Now we can calculate the perimeter of the base:
Perimeter of Base = 2 * (length + width) = 2 * (15 m + 12 m) = 2 * 27 m = 54 m
Using the formula for surface area, we have:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Surface Area = 180 m^2 + (0.5 * 54 m * 21.63 m)
Surface Area ≈ 180 m^2 + (0.5 * 54 m * 21.63 m)
Surface Area ≈ 180 m^2 + 583.74 m^2
Surface Area ≈ 763.74 m^2
Therefore, the surface area of the rectangular pyramid is approximately 763.74 square meters.
What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth.
To find the surface area of a square pyramid, we need to calculate the areas of the individual faces and then add them up.
The formula for the surface area of a square pyramid is:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Given that the base edge is 1.5 cm and the slant height is 4 cm, we can calculate the surface area.
The base of the pyramid is a square, so the base area is:
Base Area = base edge^2 = (1.5 cm)^2 = 2.25 cm^2
To calculate the perimeter of the base, we multiply the base edge by 4 since it is a square:
Perimeter of Base = 4 * base edge = 4 * 1.5 cm = 6 cm
Now we can calculate the surface area using the formula:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Surface Area = 2.25 cm^2 + (0.5 * 6 cm * 4 cm)
Surface Area = 2.25 cm^2 + (0.5 * 24 cm^2)
Surface Area = 2.25 cm^2 + 12 cm^2
Surface Area = 14.25 cm^2
Therefore, the surface area of the square pyramid is approximately 14.25 square centimeters.