Perimeter: Step-by-Step Guide
The perimeter of a shape is the distance all the way around it. To find it, add up the lengths of all the sides. Some shapes have shortcuts. For a rectangle, use 2 x (length + width). For a square, multiply one side by 4.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Identify the shape and its sides. Figure out what shape you have and write down the length of every side. Mark any sides that are equal.\[\text{sides: } s_1, s_2, \dots, s_n\]
- Choose the perimeter formula. For any shape, add up all the sides. A rectangle is 2 x (length + width). A square is 4 x side. A shape with all equal sides is the number of sides times one side.\[P = \sum_{i=1}^n s_i,\; P_{\text{rect}} = 2(l + w),\; P_{\text{reg}} = ns\]
- Put in the numbers and add. Fill in the side lengths and work out the answer.\[P = 2(l + w)\]
- Write the units. Perimeter is a length, so use the same units as the sides, like cm, m, or inches.\[P = \text{value units}\]
Worked example
A rectangle has length 15 cm and width 9 cm. Find its perimeter.
Step 1: The shape is a rectangle. The length is 15 cm and the width is 9 cm.
Step 2: Use the formula: perimeter = 2 x (length + width).
Step 3: Put in the numbers: perimeter = 2 x (15 + 9).
Step 4: Add inside the parentheses: 15 + 9 = 24.
Step 5: Multiply: 2 x 24 = 48.
Step 6: Add the units: the perimeter is 48 cm.
Check: Add all four sides: 15 + 9 + 15 + 9 = 48 cm. It matches.
Tips and common mistakes
- Perimeter is measured in regular units like cm, m, or inches. Do not use square units.
- If the shape is not regular, add every side. Do not guess that sides are equal unless the problem says so.
- If all the sides are equal, multiply one side by the number of sides.
- Make sure every side uses the same unit before you add.
- For shapes made of smaller shapes, only count the outside edges.
- A rectangle has two long sides and two short sides. That is why the formula is 2 x (length + width).
- Draw the shape and check off each side as you add it so you do not skip one or count it twice.