Content

• To step
• Method 1 of 4: Determine the perimeter of a rectangle with its length and width
• Method 2 of 4: Calculate the perimeter of the area and one side
• Method 3 of 4: Finding the outline of a compound rectangle
• Method 4 of 4: Determining the outline of a compound rectangle with limited information
• Necessities

The perimeter of a rectangle is the total length of all sides of a rectangle added together. A rectangle is defined as a quadrilateral or geometric shape with four sides. In a rectangle, both opposite sides are congruent, which means that they have the same length. While not all rectangles are square, all squares are rectangles, and a compound shape can consist of multiple rectangles.

To step

Method 1 of 4: Determine the perimeter of a rectangle with its length and width

1. Write down the standard formula for determining the perimeter of a rectangle. This formula will help calculate the perimeter of your rectangle. The standard formula is: P = 2 * (l + w).
   • Perimeter is always the total distance around the outer edge of a shape, be it a simple or compound shape.
   • This equation states P. for the "outline," l for the length and w refers to the width of the rectangle.
   • The length always has a greater value than the width.
   • Since opposite sides of a rectangle are equal, both lengths and widths will be equal. That's why you write this equation as multiplication of the sum of the length and width by 2.
   • You can also write the equation as P = l + l + w + w to make this even clearer.
2. Determine the length and width of your rectangle. For standard math problems at school, the length and width of the rectangle will always be given. These are usually next to the picture of the rectangle.
   • If you want to calculate the circumference of a rectangle in real life, use a ruler, measuring stick, or tape measure to determine the length and width of the area you are trying to calculate. If you are measuring outside, measure all sides to make sure all sides are really congruent.
   • For instance, l = 14 centimeters (5.5 in), w = 8 centimeters (3.1 in).
3. Add the length and width together. After determining the length and width, you can enter them in the equation for the circumference, in the place of the variables "l" and "w".
   • When working out the perimeter equations, keep in mind that according to the calculation order, math expressions in parentheses are solved first. So you start solving the equation by adding the length and width.
   • For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22).
4. Multiply the sum of the length and width by two. If you look at the formula for the perimeter of a rectangle, you can see that (l + w) is multiplied by two. Once you have rounded this multiplication, you have calculated the perimeter of your rectangle.
   • This multiplication takes into account the other two sides of your rectangle. When you add the width and length together, you only add the two sides of the shape.
   • Since the other two sides of the rectangle are equal to the two that have already been added together, you can simply multiply these dimensions by two to find the sum of all four sides.
   • For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22) = 44 centimeters (17.3 in).
5. Tel l + l + w + w together. Instead of adding two sides of your rectangle and multiplying them by two, you can simply add all four sides together to find the perimeter of your rectangle.
   • If you find this perimeter theory difficult to understand, this is a great place to start.
   • For example, P = l + l + w + w = ​​14 + 14 + 8 + 8 = 44 centimeters (17.3 in).

Method 2 of 4: Calculate the perimeter of the area and one side

1. Write down the formula for the area and the formula for the perimeter of a rectangle. Even though you already know the area of ​​the rectangle in this problem, you will still need to use the area formula to find the missing data.
   • The area of ​​a rectangle is a measure of the two-dimensional space in the rectangle, or the number of square units within the rectangle.
   • The formula for the area of ​​a rectangle is A = l * w.
   • The formula for the perimeter of a rectangle is P = 2 * (l + w)
   • In the above formulas it says a for "area", P. for "outline", l for the length of the rectangle, and w for the width of the rectangle.
2. Divide the total area by the total of the sides you know. This will help you find the size of the missing side of your rectangle, be it the length or the width. Finding the missing data will then allow you to calculate the circumference.
   • Since you're multiplying the length and width to find the area, you can find the length by dividing the area by the width. Likewise, dividing the area by the length will give you the width.
   • For instance, a = 112 centimeters (44.1 in) squared, l = 14 centimeters (5.5 in)
     • A = l * w
     • 112 = 14 * w
     • 112/14 = w
     • 8 = w
3. Add the length and width together. Now that you know the dimensions of both the length and the width, you can enter these values ​​in the formula for the rectangle's perimeter.
   • In this problem, you first add the length and width together, because this part of the equation is in parentheses.
   • According to the calculation order, you always work out the part between brackets first.
4. Multiply the sum of the length and width by two. Once you have added the length and width of your rectangle, you can find the circumference by multiplying the answer by two. The other two sides of the rectangle are therefore included in the calculation.
   • You can find the perimeter of the rectangle by adding the length and width and then multiplying the sum by two, because the length of the opposite sides of a rectangle is the same.
   • Both lengths of the rectangle are the same, and both widths are the same.
   • For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeters (17.3 in).

Method 3 of 4: Finding the outline of a compound rectangle

1. Write down the basic formula for the circumference. Perimeter is the sum of all outer sides of a given shape, including irregular and compound shapes.
   • A standard rectangle has four sides. The two sides that make up the length are equal to each other, and the two sides that make up the width are equal to each other. Therefore the circumference is the sum of these four sides.
   • A compound rectangle has at least 6 sides. Think of a shape such as a capital letter "L" or "T". The top "branch" can be split into a rectangle and the bottom "beam" into another. However, the outline of this shape does not depend on breaking the compound rectangle into two separate rectangles. Instead, the outline is simply: P = s1 + s2 + s3 + s4 + s5 + s6.
   • Each "s" represents a different side of the compound rectangle.
2. Determine the size of each side. In a standard calculation problem, the dimensions of all sides are usually given.
   • This example uses the abbreviations L, W, l1, l2, w1 and w2. The capital letters L. and W. represent the full lengths and widths of the shape. The lowercase letters ls and ws stand for the shorter lengths and widths.
   • Hence, the formula P = s1 + s2 + s3 + s4 + s5 + s6 equal to P = L + W + l1 + l2 + w1 + w2.
   • Variables such as "w" or "l" are simply representations of unknown numerical values.
   • Example: L = 14 centimeters (5.5 in), W = 10 centimeters (3.9 in), l1 = 5 centimeters (2.0 in), l2 = 9 centimeters (3.5 in), w1 = 4 centimeters (1.6 in), w2 = 6 centimeter (2.4 in)
     • Note that l1 and l2 being equal to L.. Likewise, it is w1 and w2 being equal to W..
3. Add all sides together. By entering the numeric values ​​of the sides into your equations, you are able to determine the perimeter of the compound shape.
   • P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 centimeters (18.9 in)

Method 4 of 4: Determining the outline of a compound rectangle with limited information

1. Organize the information you do have. You can always find the outline of a compound rectangle as long as you have at least one full length or full width, and at least three of the smaller widths or lengths.
   • For an "L" -shaped compound rectangle, use the formula P = L + W + l1 + l2 + w1 + w2
   • This formula states P. for the "outline". The uppercase letter L. and W. represent the full lengths and widths of the full assembled shape. The lowercase letters l and w represent the smaller lengths and widths in the compound form.
   • Example: L = 14 centimeters (5.5 in), l1 = 5 centimeters (2.0 in), w1 = 4 centimeters (1.6 in), w2 = 6 centimeters (2.4 in); missing: W, 12
2. Use the dimensions you need to find to find the missing dimensions of the sides. In this example, the full length, L., equal to the sum of l1 and l2. Likewise is the full width W., equal to the sum of w1 and w2. Using the same knowledge, you can add and subtract the dimensions you do have to find the two missing dimensions.
   • Example: L = l1 + l2; W = w1 + w2
     • L = l1 + l2
     • 14 = 5 + 12
     • 14 - 5 = 12
     • 9 = 12
     • W = w1 + w2
     • W = 4 + 6
     • W = 10
3. Add the sides together. Once you've done the subtraction sums to find the missing dimensions, you can add all sides together to find the perimeter of the compound rectangle. You now use the original circumference formula.
   • P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 centimeters (18.9 in)

Necessities

• Pencil
• Paper
• Calculator (optional)
• Ruler, measuring stick or a tape measure (if you want to measure an actual circumference)