The perimeter of a rectangle is the sum of the length of all its sides. A rectangle is defined as a quadrilateral, a geometric figure with four sides. In it, the sides are congruent, that is, they have the same length in pairs. While not all rectangles are squares, squares can be considered rectangles, and a compound figure can be a combination of rectangles.
Steps
Method 1 of 4: Find the Perimeter with Base and Height
Step 1. Write the basic formula for finding the perimeter of a rectangle
This formula will help you calculate the perimeter of your geometric figure: P = 2 x (b + h).
- The perimeter is always the total length of the outline of a figure, whether it is simple or composed.
- In this formula, "P" is the perimeter, "b" is the base of the rectangle and "h" its height.
- The base always has a higher value than the height.
- Since opposite sides of a rectangle are equal, both bases and heights have the same value. That's why you can write the formula as the sum of length and height multiplied by 2.
- To reaffirm this concept, it is also possible to write the equation in this way: "P = b + b + h + h".
Step 2. Find the height and base of your rectangle
In a simple school math problem, base and pitch will be part of the problem data. You will usually find the values next to the rectangle drawing.
- If you are calculating the perimeter of a real rectangle, use a ruler or tape measure to find the base and height values. If you're dealing with a natural object, measure all sides of the surface to make sure they are truly congruent.
- For example, "b" = 14 cm, "h" = 8 cm.
Step 3. Add base and height
When you have the base and height measurements, replace them with the unknowns "b" and "h".
- When working out the perimeter formula, remember that according to the rules of the order of mathematical operations, the expressions contained in brackets must be calculated before those outside. For this reason, you will start solving the equation by adding base and height.
- For example: P = 2 x (b + h) = 2 x (14 + 8) = 2 x (22).
Step 4. Multiply the sum of base and height by two
In the formula for the perimeter of the rectangle, the expression "(b + h)" is multiplied by 2. Carrying out the multiplication we obtain the perimeter of the rectangle.
- This multiplication takes into account the other two sides of the rectangle. By adding the base and height, you only used two of the four sides.
- Since the other two sides of the rectangle are the same as those already added, you just need to multiply their overall size by two to get the perimeter.
- For example P = 2 x (b + b) = 2 x (14 + 8) = 2 x (22) = 44 cm.
Step 5. Add "b + b + h + h"
Instead of adding two sides of the rectangle and multiplying the result by two, you can simply add all four sides directly to find the perimeter of the rectangle.
- If you have trouble understanding the concept of perimeter, start with this formula.
- For example P = b + b + h + h = 14 + 14 + 8 + 8 = 44 cm.
Method 2 of 4: Calculate the Perimeter Using the Area and a Side
Step 1. Write the formula for the area and perimeter of the rectangle
Even if you already know the area of the rectangle in this problem, you will still need the formula to find the missing information.
- The area of a rectangle is the measure of the two-dimensional space surrounded by the perimeter of the geometric figure, or the number of square units within it.
- The formula used to find the area of the rectangle is "A = b x h".
- The formula for the perimeter of the rectangle is "P = 2 x (b + h)".
- In the previous formulas "A" is the area, "P" is the perimeter, "b" is the base of the rectangle and "h" its height.
Step 2. Divide the total area by the side you know
This will allow you to find the measurement of the missing side of the rectangle, whether it is the height or the base. Finding this missing information you will be able to calculate the perimeter.
- To find the area you need to multiply the base and the height, so dividing the area by the height gives you the base. Similarly, dividing the area by the base gives the height.
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For example "A" = 112 square cm, "b" = 14 cm.
- A = b x h
- 112 = 14 x h
- 112/14 = h
- 8 = h
Find the Perimeter of a Rectangle Step 8 Step 3. Add base and height
Now that you know the base and height measurements, you can substitute them for the unknowns in the perimeter of the rectangle formula.
- You need to start solving the problem by adding the base and height, which are in parentheses.
- According to the order of mathematical operations, you must always solve the parts of an equation in parentheses first.
Find the Perimeter of a Rectangle Step 9 Step 4. Multiply the sum of base and height by two
After adding the base and height, you can find the perimeter by multiplying the result by two. This is to consider the other two sides of the rectangle.
- You can calculate the perimeter of the rectangle by adding the base and height, then multiplying the result by two, because the sides of the figure are equal in pairs.
- The heights and bases of the rectangle are identical to each other.
- For example P = 2 x (14 + 8) = 2 x (22) = 44 cm.
Method 3 of 4: Calculate the Perimeter of a Compound Rectangle
Find the Perimeter of a Rectangle Step 10 Step 1. Write the basic formula of the perimeter
The perimeter is the sum of all sides of any shape, including irregular and compound ones.
- A standard rectangle has four sides. The two "base" sides are equal to each other and the two "height" sides are equal to each other. Consequently, the perimeter is the sum of these four sides.
- A compound rectangle has at least six sides. Think capital "L" or "T". The top can be separated into one rectangle and the bottom into another. To calculate the perimeter of this figure, however, it is not necessary to divide the compound rectangle into two separate rectangles. The formula instead is simply: P = l1 + l2 + l3 + l4 + l5 + l6.
- Each "l" represents a different side of the compound rectangle.
Find the Perimeter of a Rectangle Step 11 Step 2. Find the measurements of each side
In a classic math school problem, you should have the measurements of all sides of the compound rectangle available.
- This example uses the abbreviations "B, H, b1, b2, h1 and h2". The uppercase "B" and "H" represent the total base and height of the figure. The tiny ones are the smallest bases and heights.
- Consequently, the formula "P = l1 + l2 + l3 + l4 + l5 + l6" becomes "P = B + H + b1 + b2 + h1 + h2".
- Variables like "b1" or "h1" are simple unknowns that represent unknown numerical values.
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Example: B = 14cm, H = 10cm, b1 = 5cm, b2 = 9cm, h1 = 4cm, h2 = 6cm.
Note that the sum of "b1" and "b2" equals "B". Similarly, "h1" + "h2" = "H"
Find the Perimeter of a Rectangle Step 12 Step 3. Add all sides together
By substituting the measurements of the sides to the unknowns of the equation, you will be able to find the perimeter of the compound figure.
P = B + H + b1 + b2 + h1 + h2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 cm
Method 4 of 4: Measure the Perimeter of a Compound Rectangle with Limited Information
Find the Perimeter of a Rectangle Step 13 Step 1. Reorder the information you know
If you have at least one of the total lengths and at least three of the shorter lengths, it is still possible to calculate the perimeter of a compound rectangle.
- For an "L" shaped rectangle, use the formula "P = B + H + b1 + b2 + h1 + h2".
- In this formula "P" stands for "perimeter". The uppercase "B" and "H" are the total base and height of the entire compound shape. The lowercase "b" and "h" are the shortest bases and heights.
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Example: B = 14 cm, b1 = 5 cm, h1 = 4 cm, h2 = 6 cm; missing data:
H, b2.
Find the Perimeter of a Rectangle Step 14 Step 2. Use the known measurements to find the missing sides
In this example, the total base "B" is equal to the sum of "b1" and "b2". Similarly, the total height "H" equals the sum "h1" and "h2". Thanks to these formulas, you can add and subtract the measures you know to get the missing ones.
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Example: B = b1 + b2; H = h1 + h2.
- B = b1 + b2
- 14 = 5 + b2
- 14 - 5 = b2
- 9 = b2
- H = h1 + h2
- H = 4 + 6
- H = 10
Find the Perimeter of a Rectangle Step 15 Step 3. Add the sides
Once you find the missing measurements, you can add all sides to get the perimeter of the compound rectangle, using the original perimeter formula.
P = B + H + b1 + b2 + h1 + h2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 cm
