Perimeter is always the total distance around the outside edge of any shape, whether it is simple or compound. In this equation, P stands for “perimeter,” l refers to the length of the rectangle, and w refers to the width of the rectangle. Length always has a greater value than width. Because opposite sides of a rectangle are equal, both lengths will be the same and both widths will be the same. This is why you write the equation as a 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 very clear.

If you are calculating the perimeter of a rectangle in real life, use a ruler, yardstick, or tape measure to find the length and width of the area that you are trying to measure. If you’re measuring outdoors, measure all sides to see if the opposites are truly congruent. For example, l = 14 centimeter (5. 5 in), w = 8 centimeter (3. 1 in).

When you are working out your perimeter equations, note that according to the order of operations, mathematical expressions contained inside brackets or parentheses are solved before those outside of the parentheses. [7] X Research source So, you’ll begin solving your equation by adding the length and width. For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22).

This multiplication takes into account the other two sides of your rectangle. When you added together the width and length, you only added together two sides of the shape. Since the other two sides of the rectangle are equal to the two already added together, you can simply multiply this measurement by two in order to find the total sum of all four sides. For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17. 3 in).

If you struggle with the concept of perimeter, this is a great place to start. For example, P = l + l + w + w = 14 + 14 + 8 + 8 = 44 centimeter (17. 3 in).

The area of a rectangle is a measurement of the two-dimensional space within the rectangle, or the number of square units within the rectangle. The formula used to find the area of a rectangle is A = l * w. The formula used to find the perimeter of a rectangle is P = 2 * (l + w) In the above formulas, A stands for “area,” P stands for “perimeter,” l refers to the length of the rectangle, and w refers to the width of the rectangle.

Because you multiply the length and width together to find the area, dividing the area by the width will give you the length. Likewise, dividing the area by the length will give you the width. For example, A = 112 centimeter (44. 1 in) squared, l = 14 centimeter (5. 5 in) A = l * w 112 = 14 * w 112/14 = w 8 = w

In this problem, you add length and width together first because this part of the equation occurs in parentheses. According to the order of operations, you always do the part of the equation in parentheses first.

You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17. 3 in).

A standard rectangle has four sides. The two sides composing the length are equal to each other, and the two sides composing the width are equal to each other. Therefore, the perimeter is the sum of those four sides. A compound rectangle has at least six sides. Think of a capital “L” or “T” shape. The top “branch” can be separated into one rectangle and the bottom “bar” can be separated into another. The perimeter of this shape, however, does not rely on breaking up the compound rectangle into two separate rectangles. Instead, the perimeter is simply: P = s1 + s2 + s3 + s4 + s5 + s6. Each “s” represents a different side of your compound rectangle.

This example uses the abbreviations L, W, l1, l2, w1, and w2. The uppercase L and W stand for the full lengths and widths of the shape. The lowercase ls and ws stand for the smaller lengths and widths. As such, the formula P = s1 + s2 + s3 + s4 + s5 + s6 equals P = L + W + l1 + l2 + w1 + w2. Variables, like “w” or “l” are simply placeholders for unknown numeric values. [14] X Research source Example: L = 14 centimeter (5. 5 in), W = 10 centimeter (3. 9 in), l1 = 5 centimeter (2. 0 in), l2 = 9 centimeter (3. 5 in), w1 = 4 centimeter (1. 6 in), w2 = 6 centimeter (2. 4 in) Note that l1 and l2 will equal L. Similarly, w1 and w2 will equal W.

P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 centimeter (18. 9 in)

For an “L”-shaped compound rectangle, use the formula P = L + W + l1 + l2 + w1 + w2 In this formula, P stands for “perimeter. ” The uppercase L and W stand for the full lengths and widths of the entire compound shape. The lowercase ls and ws stand for the smaller lengths and widths in the compound shape. Example: L = 14 centimeter (5. 5 in), l1 = 5 centimeter (2. 0 in), w1 = 4 centimeter (1. 6 in), w2 = 6 centimeter (2. 4 in); missing: W, l2

Example: L = l1 + l2; W = w1 + w2 L = l1 + l2 14 = 5 + l2 14 – 5 = l2 9 = l2 W = w1 + w2 W = 4 + 6 W = 10

P = L + W + l1 + l2 + w1 + w2 = 14 + 10 + 5 + 9 + 4 + 6 = 48 centimeter (18. 9 in)