Perimeter is a fundamental concept in geometry that helps us understand the measurement of shapes. Whether you’re a student just starting to learn about shapes or someone looking to refresh your math skills, understanding How To Find The Perimeter is essential. This guide will break down the concept of perimeter, explain how to calculate it for various shapes, and provide practical examples to solidify your understanding.
Understanding Perimeter: The Distance Around
The perimeter of any two-dimensional (2D) shape is simply the total distance around its outer boundary. Imagine walking around the edge of a park or a garden; the total distance you walk is the perimeter of that area. Perimeter is always measured in linear units, such as inches, feet, centimeters, or meters, depending on the units used for the sides of the shape.
Let’s visualize this with a simple example:
In the square above, each side is one unit long. To find the perimeter, we start at one corner (vertex) and add the length of each side as we move around the shape until we return to our starting point. In this case, it’s 1 + 1 + 1 + 1 = 4 units.
Consider a rectangle:
By counting the units along each side, we can find the perimeter. Starting at a corner and moving around, we count 6 units, then 4 units, then 6 units again, and finally 4 units to close the shape. Adding these together: 6 + 4 + 6 + 4 = 20 units. Therefore, the perimeter of this rectangle is 20 units.
Notice that we can also find the perimeter by simply adding the lengths of all the sides. This addition method is the core principle for calculating the perimeter of any polygon.
Calculating Perimeter for Different Shapes
The basic method for finding the perimeter is to add up the lengths of all the sides. Let’s explore how this applies to different common shapes:
Perimeter of Polygons: Adding All Sides
For any polygon (a closed shape with straight sides), the perimeter is found by adding the lengths of all its sides. This rule applies to triangles, quadrilaterals (like squares, rectangles, parallelograms, trapezoids), pentagons, hexagons, and any polygon with more sides.
Example 1: Triangle Perimeter
To find the perimeter of a triangle with sides of 5 cm, 12 cm, and 13 cm, we simply add these lengths:
Perimeter = 5 cm + 12 cm + 13 cm = 30 cm
Example 2: Parallelogram Perimeter
A parallelogram has opposite sides of equal length. If a parallelogram has sides of 8 units and 4 units, we calculate the perimeter as:
Perimeter = 8 units + 4 units + 8 units + 4 units = 24 units
When units are not specified (like cm, m, km), we generally label the perimeter as ‘units’.
Step-by-Step Guide: How to Find the Perimeter
To summarize the process of finding the perimeter of any polygon:
- Identify all side lengths: Measure or find the given lengths of each side of the shape.
- Add the side lengths: Sum up the lengths of all the sides.
- State the answer with units: Write down the total sum along with the correct unit of measurement (inches, feet, cm, m, units, etc.).
Free Perimeter Quiz for Practice
Want to test your understanding? Take this free Perimeter Check for Understanding Quiz designed for grades 3 to 4. It features over 10 questions with answers covering various perimeter concepts to help identify areas where you excel and where you might need more practice.
DOWNLOAD FREE PERIMETER QUIZ
Perimeter Examples: Putting It Into Practice
Let’s work through some examples to illustrate how to find the perimeter in different scenarios.
Example 1: Perimeter of a Rectangle on a Grid
What is the perimeter of the rectangle shown on the grid?
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Add all side lengths:
- Length of the rectangle = 7 units
- Width of the rectangle = 5 units
- Rectangles have opposite sides of equal length.
- Perimeter = 7 + 5 + 7 + 5
-
Write the final answer with correct units:
- Perimeter = 7 + 5 + 7 + 5 = 24
- Units are not specified, so we use ‘units’.
- The perimeter of the rectangle is 24 units.
Example 2: Finding a Missing Side Length Given the Perimeter
The perimeter of a rectangle is 78 meters. One side length is 34 meters. Find the missing side length.
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Add all side lengths (with unknowns):
- Let the unknown side length be ‘x’.
- Perimeter = 34 m + x + 34 m + x = 78 m
- Combine known sides: 34 m + 34 m = 68 m
- So, 68 m + 2x = 78 m
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Solve for the missing side length:
- Subtract 68 m from the total perimeter: 78 m – 68 m = 10 m
- This 10 m is the combined length of the two missing sides (2x).
- Divide 10 m by 2 to find the length of one missing side: 10 m / 2 = 5 m
-
Write the final answer with correct units:
- The missing side length is 5 meters.
Example 3: Perimeter of an Isosceles Triangle
What is the perimeter of the isosceles triangle shown?
-
Add all side lengths:
- Perimeter = 11 inches + 11 inches + 9 inches = 31 inches
-
Write the final answer with correct units:
- The perimeter of the triangle is 31 inches.
Example 4: Perimeter of a Trapezoid
What is the perimeter of the trapezoid?
-
Add all side lengths:
- Perimeter = 8 cm + 5 cm + 6 cm + 5 cm = 24 cm
-
Write the final answer with correct units:
- The perimeter of the trapezoid is 24 cm.
Example 5: Perimeter of a Rectilinear Shape (Polygon on a Grid)
What is the perimeter of the polygon on the grid?
-
Add all side lengths (by counting units):
- Count each unit around the shape, starting from a point and marking it to avoid double counting.
-
Write the final answer with correct units:
- By counting, we find the perimeter to be 36 units.
- The perimeter of the polygon is 36 units.
Example 6: Perimeter of a Complex Rectilinear Shape with Missing Sides
Find the perimeter of the polygon with missing side lengths.
-
Add all side lengths (including finding missing lengths):
- Use the properties of rectangles to find missing sides.
- The vertical missing side: 8 m – 5 m = 3 m.
- The horizontal missing side: 10 m + 13 m = 23 m.
-
Add all known and calculated side lengths:
- Perimeter = 8 m + 10 m + 3 m + 13 m + 5 m + 23 m = 62 m
-
Write the final answer with correct units:
- The perimeter of the polygon is 62 meters.
Teaching Tips for Perimeter
- Variety of Shapes: Use worksheets with a mix of regular and irregular shapes, gridded and non-gridded figures. This helps students practice different strategies and choose the most effective one for each shape type.
- Pattern Recognition: Encourage students to identify patterns. For example, triangles always have 3 sides to add, quadrilaterals have 4, and so on. Connect this to formulas for regular shapes where sides are equal.
- Real-World Connections: Relate perimeter to real-life situations like fencing a garden, framing a picture, or measuring a room’s baseboards.
Common Mistakes to Avoid
- Order of Addition: Students sometimes worry about the order in which they add sides. Emphasize that addition is commutative; the order doesn’t matter as long as all sides are included once.
- Perimeter vs. Area: Confusion between perimeter and area is common. Clearly differentiate between “distance around” (perimeter) and “space inside” (area). Use visual aids and hands-on activities to reinforce these concepts.
- Units Confusion: Mixing up units or forgetting units is another common error. Remind students to always include units in their answers and to ensure all side lengths are in the same unit before adding.
- Incorrect Formulas: While adding all sides always works, formulas can be useful for regular shapes. Ensure students understand when and how to use formulas correctly and don’t confuse them with area formulas.
Practice Perimeter Questions
Test your skills with these practice questions:
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What is the perimeter of the rectangle?
- 24 units (Correct Answer)
- 20 units
- 12 units
- 4 units
Explanation: Perimeter = 10 units + 2 units + 10 units + 2 units = 24 units.
-
The perimeter of the rectangle is 94 cm. Find the missing side length.
- 26 cm (Correct Answer)
- 24 cm
- 42 cm
- 52 cm
Explanation: Missing side length = (94 cm – (21 cm + 21 cm)) / 2 = 26 cm.
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What is the perimeter of the hexagon?
- 36 ft (Correct Answer)
- 26 ft
- 40 ft
- 32 ft
Explanation: Perimeter = 10 ft + 4 ft + 4 ft + 10 ft + 4 ft + 4 ft = 36 ft.
-
What is the perimeter of the regular pentagon?
- 35 inches (Correct Answer)
- 7 inches
- 49 inches
- 28 inches
Explanation: Perimeter = 7 inches + 7 inches + 7 inches + 7 inches + 7 inches = 35 inches.
-
What is the perimeter of the polygon?
- 28 units (Correct Answer)
- 24 units
- 26 units
- 30 units
Explanation: Count the units around the shape on the grid to find the perimeter of 28 units.
-
What is the perimeter of the polygon?
- 108 ft (Correct Answer)
- 78 ft
- 102 ft
- 82 ft
Explanation: Calculate missing sides and add all sides: 6 ft + 29 ft + 25 ft + 11 ft + 19 ft + 18 ft = 108 ft.
Perimeter FAQs
When will students learn to find perimeters of more complex shapes?
In higher grades, students will explore the perimeter of circles (circumference) and use coordinate geometry and the distance formula to find perimeters of more complex polygons, both regular and irregular.
How are area and perimeter of a rectangle related?
While both area and perimeter use the dimensions of length and width of a rectangle, they measure different aspects. Perimeter is the distance around, measured in linear units. Area is the space enclosed within the rectangle, measured in square units.
How are area and perimeter of a triangle related?
Similar to rectangles, perimeter of a triangle is the distance around it (sum of sides), measured in linear units. Area is the space enclosed within the triangle, measured in square units. Different formulas and dimensions are used to calculate area and perimeter for triangles.
Next Steps in Geometry
Continue your geometry journey with these related topics:
- Symmetry
- Angles in Polygons
- Congruence and Similarity
- Prism Shapes
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