Definition Of A Rectangle
The word “rectangle” comes from the Latin word rect (right) and the Old French word angle (angle). Thus, a rectangle is a shape that contains four right angles. A rectangle also has parallel sides, which makes it a type of parallelogram. The top and bottom sides of a rectangle are always the same length, as are the left and ride sides. From this definition, we can say that every square is a rectangle because it has four right angles; however, not every rectangle is a square, since a rectangle’s length and width don’t have to be the same.
Perimeter Of A Rectangle
To find out the perimeter (P) of a rectangle, it’s necessary to know the length (L) and the width (W). Once you know those numbers, you can plug them into the formula 2L + 2W = P.
In other words, if a rectangle has a length of 8 feet and a width of 4 feet, the perimeter is (2 x 8) + (2 x 4), or 24 feet.
Area Of a Rectangle
To find out the total area (A) inside a rectangle, use the formula L x W = A. Using the numbers in the above example, an 8-foot by 4-foot rectangle has an area of 32 square feet, since 8 x 4 = 32.
Volume Of A Rectangle
Volume (V) is the space inside of a three-dimensional shape. A three-dimensional rectangle is known as a rectangular prism, and its third dimension is height. To find the volume of a rectangular prism, first measure the length, the width and the height, and then multiply those numbers in any order. The formula for this calculation is L x W x H = V.
If we take the 8 x 4-foot rectangle from the previous two examples and make it 5 feet tall, we can calculate the volume by multiplying 8 x 4 x 5, which equals 160 cubic feet.
Problems and Solutions
Problem 1: You have a yard that is 100 feet long and 50 feet wide, and you want to put a fence around it. How much fencing material do you need to buy?
Solution: To solve this problem, you need to calculate the perimeter of the yard. Using the formula 2L + 2W = P, you get (2 x 100) + (2 x 50) = 300 feet.
Problem 2: You want to build a small patio that is 10 feet long and 12 feet wide, and you plan to use 1-foot square paving stones. How many paving stones do you need to buy to cover the entire area?
Solution: To solve this problem, you need to calculate the area of the patio. Using the formula L x W = A, you get 10 x 12 = 120 square feet. Thus, you will need to buy 120 paving stones.
Problem 3: You are planning to rent a storage unit while remodeling an office. The smallest size available is 5 feet by 5 feet on the floor with a height of 8 feet. How many cubic feet of storage space will you get?
Solution: To solve this problem, you need to calculate the volume of the rectangular space enclosed by storage unit. Using the formula L x W x H = V, you get 5 x 5 x 8 = 200 cubic feet.