Janet needs a rectangular piece of cardboard measuring 21 ft by 24 ft for a school project.
a) What is the area of the cardboard in square feet?
b) What is the area of the cardboard in square yards? Show your calculations in two different ways.
c) The store charges $0.35/m2 for cardboard. How much will the cardboard Janet needs cost?
a) A = LW
b) 1 yard = 3 feet
c) Multiply your answer for b by 0.35
I'll be glad to check your answers.
To find the answers to these questions, we need some basic formulas and unit conversions.
a) The area of a rectangle is calculated by multiplying its length by its width. Therefore, to find the area of the cardboard, we multiply its length of 21 ft by its width of 24 ft:
Area = Length x Width
Area = 21 ft x 24 ft
Area = 504 square feet
So, the area of the cardboard is 504 square feet.
b) To find the area in square yards, we need to convert the measurements from feet to yards. Since 1 yard is equal to 3 feet, we can use the following conversion formulas:
1 square foot = (1/9) square yard
1 square yard = 9 square feet
Method 1:
To find the area in square yards, we divide the area in square feet by 9:
Area in square yards = Area in square feet / 9
Area in square yards = 504 square feet / 9
Area in square yards = 56 square yards
Method 2:
Alternatively, we can convert the length and width from feet to yards and then multiply them to find the area in square yards:
Length in yards = Length in feet / 3
Width in yards = Width in feet / 3
Length in yards = 21 ft / 3
Length in yards = 7 yards
Width in yards = 24 ft / 3
Width in yards = 8 yards
Area in square yards = Length in yards x Width in yards
Area in square yards = 7 yards x 8 yards
Area in square yards = 56 square yards
So, the area of the cardboard is 56 square yards.
c) To find the cost of the cardboard, we need to calculate the total area in square meters and then multiply it by the cost per square meter.
First, let's convert the area from square feet to square meters. Since 1 square meter is equal to 10.76 square feet, we can use the following formula:
1 square meter = 1 square yard x (0.9144 meters/1 yard)^2
1 square meter = 1.0936 square yard
1 square yard = (1/1.0936) square meter
1 square yard = 0.9144 square meter
The area in square meters is:
Area in square meters = Area in square yards x 0.9144 square meter/square yard
Area in square meters = 56 square yards x 0.9144 square meter/square yard
Area in square meters = 51.1656 square meters
Now, to calculate the cost, we multiply the area by the cost per square meter:
Cost = Area in square meters x Cost per square meter
Cost = 51.1656 square meters x $0.35/m2
Cost = $17.92
So, the cardboard Janet needs will cost $17.92.