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Calculating the Perimeter of a Rectangle
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1. Our Training Videos
Skills Application: Calculating the Perimeter of a Rectangle
Step-by-Step: Calculating the Perimeter of a Rectangle
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2. Running with Pi

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Two of the most popular diamond cuts are rectangular and are named “emerald” and “princess”. These cuts are widely used for different reasons. The emerald cut shows off a rocks clarity better than any other cut. For maximum brilliance, the princess cut was developed. In either designs, the rectangle's perimeter, length and width are important considerations. Mathematical transition between the two shapes is possible by slightly changing the length and width, but they also mean transitioning from the benefits of one cut to the benefits of the other.

## Running with Pi

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3. Our Training Worksheets

A rectangle has four sides and its opposite sides are equal. One pair of opposite sides is called the length and the other pair is the width. To find the perimeter of a rectangle multiply the length by two, multiply the width by two, and then add the products.

FORMULA FOR THE PERIMETER OF A RECTANGLE

Lets call P the perimeter of a rectangle having length L and with W. To find the perimeter of a rectangle add the length and the width and multiply the sum by two.

P = 2(L + W)

EXAMPLE:

Before ordering baseboard trim, the perimeter of a 12 ft x 18 ft room must be found. What is the perimeter of the room?

SOLUTION:

1. Add the length and width in the brackets. The length plus the width represent halfway around the room:

12 +18 = 30

1. Multiply the sum of the length and width by 2 to find the entire distance around.

2 x 30 = 60

The perimeter of the room is 60 ft.

Check out the ADVANCED section. The exercises will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. It is important to try alternative calculations or approaches, to sketch the shapes, label the shapes with the given numbers, tracking changes to units of measure, visualizing to cross-link the concepts of perimeter and numbers. We use the numbers from this sandbox example. If you spend 30 – 60 min working with the different ideas in the ADVANCED page, youll remember key formulas easier and youll learn new skills faster.

### A Short Review

Adding the side lengths on a rectangle could be fairly simple:

Perimeter of a rectangle = Length + Width + Length + Width

You can of course multiply:

Perimeter of a rectangle = (Length + Width) x 2

If you work in fractions, make sure you can add and multiply them without a problem.

### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Question

Example:

1.  Whats the perimeter of a rectangle, 3 units long and 2 units wide?

2.  Calculate the perimeter of a rectangle with the following side lengths. You can add or use 2(w + L) = P or any of the 6 rectangle formulas.

w = 8 ft, L = 3 ft

### Worksheet: Level 1 Answer Key

1.  3 + 3 + 2 + 2 = 10

2.  2(w + L) = P

2 × (width + length) = perimeter of rectangle

(8 + 3) = 11

2 × (11) = 22 ft.

### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Question

Example: What length of PVC edge is needed to laminate a drawer front, w = 5 in, L = 18 in?

### Worksheet: Level 2 Sample Answer

2(w + L) = P

2 × (width + length) = perimeter of rectangle

(5 + 18) = 23

2 × (23) = 46"

### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Question

Example:

How much CAUTION tape is needed to circle an area with a w = 12‘-4”, L = 27‘-10”?

### Worksheet: Level 3 Sample Answer

Watch out:

• Don’t let the word “circle” in the text confuse you. It is still a rectangular perimeter problem.
• The word area is in the text, but that doesn’t make this an area calculation. The tape has
a length around this area, meaning perimeter calculation.

2(w + L) = P

2 ×(width + length) = perimeter of rectangle

(12‘-4” + 27‘-10”) = 40‘-2”

2 × (40‘-2”) = 80‘-4”

Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

### Worksheet: Advanced Level Sample Question

Example:

Calculate the perimeter of rectangle whose side length is 7 feet and side width is 4 feet.

Calculate the perimeter of rectangle whose side length is 7 feet and side width is 4 feet.

One way to get the answer, using the formula 2(w + L) = P
Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this:

Get a \$20-or-so dual-display scientific calculator, even if you cant take it with you into the exam hall. A calculator is also a learning tool, Technology Use is one of the 9 Essential Skills you cant do without.

Using a scientific calculator, do the following:
Enter 2
Press x (multiplication) button (this could be omitted, depending on your calculators circuits)
Press (
Enter 4
Press + button
Enter 7
Press )
Press =
You should see 22 on your display.

Calculate the perimeter of rectangle whose side length is 7 feet and side width is 4 feet.

Another way to get the answer, using the formula 2(w + L) = P:
1. Identify that the perimeter is to be calculated.

2. Recognize that the perimeter of a shape can be calculated by the formula 2(w + L).

3. Recognize that addition inside the bracket comes before multiplication by 2.

4. So, lets  set up the problem to work inside the bracket:

length + width = half the perimeter

1. Calculate:             7     +    4     = 11

2. Take a pencil and write down  “half the perimeter = 11” or “P/2 = 11”

1 length + 1 width goes around the rectangle only halfway around. The other half needs to be counted as well.

1. Set up to finish the rest of the problem outside the bracket:

2 x half perimeter = perimeter

1. Calculate:        2 x          11             = 22

2. Take a pencil and write down  “perimeter = 22” or “P = 22”

3. Write ft or  sign or feet after the number 22 Now youre done with the math.

4. The last step: check your work, make sure everything was copied and written correctly then determine that the correct way to write the answer is 22 ft or 22 or 22 feet

1. Identify that the perimeter is to be calculated.

2. Recognize that the perimeter of a shape can be calculated by addition.

3. Set up the problem:

length + width + length + width = perimeter

1. Calculate:             7     +    4      +     7      +     4     = 22

2. Take a pencil and write down  “perimeter = 22” or “P = 22”

3. Write ft or  sign or feet after the number 22 Now youre done with the math.

4. The last step: check your work, make sure everything was copied and written correctly then determine that the correct way to write the answer is 22 ft or 22 or 22 feet

1. Compare step 3 in episodes 10 & 11. Perimeter is said to be calculated by

“length + width + length + width”     in one and

“length + length + length + length”    in the other

One includes “width” the other does not. The formulas look different. But they are really not.

Why? Is there still a way that explains how these 2 different formulas are the same, consistent and valid? Look for clues in episode 09.

1. Words in English can not be meaningfully written backwards. For example:

MATH is meaningful, HTAM is not.

Formulas in math can be written backwards. The formula used in the problem is

2(w + L) = P   , same as P = (w + L) x 2

just written backwards.

A formula is a symbolic short-hand way to write procedures. Based on either of these formulas the 2-step procedure in full words looks like:

“Start inside the bracket with the WIDTH, then add LENGTH to it. This total will be doubled to come to the final result.”

1. What if you take the LENGTH first (7ft), then add WIDTH to it (4ft), then double their sum to get perimeter. Does the final answer change? Write the last sequence into a formula.

1. Compare the steps in 2) and 3) above with this formula:

P = 2W + 2L

Double the width, then double the length, then add their totals together to get perimeter. “

If L = 7 ft and w = 4 ft, does this formula P = 2W + 2L get the same results as 2(w + L) = P ?

1. Write an equation from these words: Double the length, then double the width, add them together to get perimeter.

1. The perimeter of a square is P = 4s

1. What do you think “s” stands for?

2. How is the squares formula similar and different from a rectangles? List similarities and differences.

1. Addition is commutative. So is multiplication. Definition of “commute” from a dictionary tells us that “commute = travel some distance between one's home and place of work, travel to and from work, travel to and fro, travel back and forth”

a)      So, what does commutative mean in math?

b)      Write an example using the numbers 2 and 3 showing that addition is commutative.
c)      Write an example that multiplication is commutative, using the numbers 2 and 3.
1. So now we have at least 6 possible ways to calculate the perimeter of a rectangle:

2L + 2W = P

2W + 2L  = P

(L + w) x 2 = P

(w+ L) x 2 = P

L + w + L + w =  P

w + L + w + L = P

Same results, about the same number of steps, same amount of work. Use a formula thats easiest to remember for you.

1. Length and width are synonyms, interchangeable. Their precise meaning depends on the point of view of the observer.

1. Result does not change. (L + w) x 2 = P

2. Yes

3. 2L + 2W = P

4. a) side length

b) DIFFERENCES:

To calculate the squares perimeter there is just one number to work with (s). Theres neither length or width to work with.

To calculate the rectangle`s perimeter, you have to have 2 numbers for length and width, 1 number is not enough.

SIMILARITIES: Both perimeters also possible to calculate by addition only

Square             P = s + s + s + s

Rectangle        P = L + w + L + w

or both shapes can be calculated faster by using multiplication instead of only addition:

Square             P = 4s

Rectangle        P = 2(L+W)

1. a) The numbers can change their order, the terms are interchangeable
b) 2 + 3 = 3 + 2
c) 2 x 3 = 3 X 2