4 Ways to Find the Perimeter of a Rectangle

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4 Ways to Find the Perimeter of a Rectangle
4 Ways to Find the Perimeter of a Rectangle
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The perimeter of a rectangle equals the sum total of all its sides. A rectangle is defined as quadrilateral, that is, a geometric figure with four sides. In it, both sets of opposite sides are congruent; in other words, they are the same length. While not all triangles are square, all squares can be considered rectangles, and a composite shape can be made up of rectangles.

Steps

Method 1 of 4: Finding Perimeter with Length and Width

Find the Perimeter of a Rectangle Step 1

Step 1. Write the basic perimeter formula

This equation will help you calculate the perimeter of the rectangle. The basic formula is: P = 2 * (c + l).

  • The perimeter always equals the total distance from the outer edges of any figure, whether simple or composite.
  • In this equation, P is the perimeter, c is the length, and l is the width of the rectangle.
  • Length always has a value greater than width.
  • Since the opposite sides of a rectangle are equivalent, both lengths will be equal, as will the widths. That's why the equation is multiplying the sum of length and width by two.
  • To make it clearer, you can write it as: P = c + c + l + l.
Find the Perimeter of a Rectangle Step 2

Step 2. Find the length and width of the rectangle

In mathematics didactic questions, these values ​​are given in the statement. They are usually found next to the rectangle design.

  • If you're calculating the perimeter of a rectangle in real life, use a ruler, braid, or measuring tape to find the length and width of the area you're trying to measure. When doing this, measure all sides to see if the opposite sides are really congruent.
  • For example, c = 14 cm and l = 8 cm.
Find the Perimeter of a Rectangle Step 3

Step 3. Add the length to the width

After measuring the values, substitute variables c and l in the perimeter formula.

  • When working with the perimeter formula, note that, according to the order of operations, the math expressions contained in parentheses or braces must be resolved before those outside. So start the resolution by adding the length to the width.
  • For example, P = 2 * (c + l) = 2 * (14 + 8) = 2 * (22).
Find the Perimeter of a Rectangle Step 4

Step 4. Multiply the sum of length and width by two

In the formula for the perimeter of the rectangle, the expression "(c + l)" is multiplied by two. After performing the multiplication, you will have the perimeter of the rectangle.

  • This multiplication takes into account the other two sides of the rectangle. When you add length to width, you are just adding two sides of the picture.
  • Since the other two sides of the rectangle are identical to the first two already added, just multiply this measure by two to find the sum of the four sides.
  • For example, P = 2 * (c + l) = 2 * (14 + 8) = 2 * (22) = 44 cm.
Find the Perimeter of a Rectangle Step 5

Step 5. Add c + c + l + l

Instead of adding the two sides of the rectangle and multiplying by two, you can simply add all four sides together to find the perimeter.

  • If you're having trouble understanding the concept of perimeter, this is a great way to start.
  • For example, P = c + c + l + l = 14 + 14 + 8 + 8 = 44 cm.

Method 2 of 4: Calculating Perimeter with Area and One Side

Find the Perimeter of a Rectangle Step 6

Step 1. Write the formula for the area and perimeter of a rectangle

Even if you already know the value of the rectangle's area, you'll still need to use its formula to find the requested value.

  • The rectangle's area is the measure of the two-dimensional space (or the number of square units) within it.
  • The formula used to find the area of ​​a rectangle is A = c * l.
  • The formula used to find the perimeter of a rectangle is P = 2 * (c + l).
  • In the formulas above, A is the area, "P" is the perimeter, "c" is the length, and "l" is the width of the rectangle.
Find the Perimeter of a Rectangle Step 7

Step 2. Divide the total area by the known measurement

This allows you to find the unknown side of the rectangle, be it length or width. Finding unknown information allows you to calculate the perimeter value.

  • Since the area is calculated by the product of the length and the width, dividing it by the width gives you the value of the length. Likewise, by dividing the area by the length, you get the width value.
  • For example, A = 112 cm² and c = 14 cm

    • A = c * l
    • 112 = 14 * l
    • 11214{displaystyle {frac {112}{14}}}

      = l

    • 8 = l
Find the Perimeter of a Rectangle Step 8

Step 3. Add the length to the width

Now that you know the length and width value, substitute them into the perimeter formula.

  • In this example, add the length to the width first, as they are enclosed in parentheses.
  • According to the order of operations, always start with the part inside the parentheses.
Find the Perimeter of a Rectangle Step 9

Step 4. Multiply the sum of the length and the width by two

After performing the sum inside the parentheses, multiply the result by two to find the perimeter value. This takes into account the other two sides of the rectangle.

  • You can find the perimeter of a rectangle by adding the length to the width and multiplying the result by two, because the opposite sides of this figure are equivalent.
  • The two lengths of the rectangle are identical, as are the two widths.
  • For example, P = 2 * (14 + 8) = 2 * (22) = 2 * (22) = 44 cm.

Method 3 of 4: Finding the Perimeter of a Composite Rectangle

Find the Perimeter of a Rectangle Step 10

Step 1. Write the basic perimeter formula

The perimeter is the sum total of the outsides of any figure, including composite and irregular shapes.

  • A regular rectangle has four sides. The two sides that make up the length are equivalent, as are the two sides of the width. Therefore, the perimeter is the sum of the four sides.
  • A composite rectangle has at least six sides. Think of the shape of the capital letters "L" and "T". The upper part can be separated from the lower part, forming two rectangles. The perimeter of this shape, however, does not depend on breaking the composite rectangle into two separate rectangles. Instead, the formula is: P = s1 + s2 + s3 + s4 + s5 + s6.
  • Each "s" represents a different side of the composite rectangle.
Find the Perimeter of a Rectangle Step 11

Step 2. Find the measurement on each side

In a didactic math problem, measurements of all sides are usually given in the statement.

  • The following example uses the following abbreviations C, L, c1, c2, l1 and l2. The capital letters C and L represent, respectively, the total lengths and widths of the figure. The lowercase letters c and l represent, respectively, the smallest values ​​of lengths and widths.
  • Thus, the formulas P = s1 + s2 + s3 + s4 + s5 + s6 and P = C + L + c1 + c2 + l1 + l2 are equal.
  • Variables, like l and "c, are just placeholders for unknown numeric values.
  • Example: C = 14 cm, L = 10 cm, c1 = 5 cm, c2 = 9 cm, l1 = 4 cm, l2 = 6 cm

    Note that c1 and c2 are equivalent to C. Likewise, l1 and l2 equal L

Find the Perimeter of a Rectangle Step 12

Step 3. Add the values ​​from all sides

After replacing the numerical values ​​in the formula, you will find the perimeter value of the composite figure.

  • P = C + L + c1 + c2 + l1 + l2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 cm

Method 4 of 4: Measuring the Perimeter of a Composite Rectangle Without All Measurements

Find the Perimeter of a Rectangle Step 13

Step 1. Organize the known measurements

You can still find the perimeter of a composite rectangle as long as you know at least the total width or length value, and at least three smaller measurement values.

  • For a composite rectangle in the shape of "L", use the formula P = C + L + c1 + c2 + l1 + l2
  • In this formula, P represents the perimeter measure. The capital letters C and L represent, respectively, the total lengths and widths of the composite figure. The lowercase letters c and l represent, respectively, the smaller values ​​of the lengths and widths of the composite figure.
  • Example: C = 14 cm, c1 = 5 cm, l1 = 4 cm, l2 = 6 cm; unknown:

    L, c2

Find the Perimeter of a Rectangle Step 14

Step 2. Use known measurements to find unknown measurements

In the example above, the total measure of length, C, will equal the sum of c1 and c2. Likewise, the total measure of width, L, will equal the sum of l1 and l2. Using this knowledge, add and subtract the known measures to find the two unknown measures.

  • Example: C = c1 + c2; L = l1 + l2

    • C = c1 + c2
    • 14 = 5 + c2
    • 14 - 5 = c2
    • 9 = c2
    • L = l1 + l2
    • L = 4 + 6
    • L = 10
Find the Perimeter of a Rectangle Step 15

Step 3. Add the values

By subtracting to find the unknown measure, you can add all sides together and find the perimeter of the composite rectangle. It is now possible to use the original formula.

  • P = C + L + c1 + c2 + l1 + l2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 cm

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