Find Perimeter Using A Grid

🔑 Key Concepts

• Perimeter is the total distance around the outside of a figure.
• For an irregular shape on a grid, count the length of each outside side segment.
• Be careful not to include any interior space that is not part of the boundary.
• Organizing the side lengths before adding helps prevent missing a segment.
• If no unit is given, write the answer in units.

✏️ Worked Examples — Perimeter of an Irregular Shape on a Grid

Step 1 — Count the Outside Sides

Find the perimeter of the irregular shape shown below.

First, trace only the outside boundary of the figure. This shape has 8 sides.

To find the perimeter, determine the length of each outside side and then add those lengths together.

Count carefully around the shape in one direction so that no side is skipped or counted twice.

Step 2 — Record the Length of Each Side

Use the labeled image to record each side length.

The 8 outside side lengths are:

\(6,\ 7,\ 4,\ 3,\ 1,\ 2,\ 3,\ 2\)

Write an addition expression containing every outside side.

\(P=6+7+4+3+1+2+3+2\)

Step 3 — Add the Side Lengths

Add the side lengths in groups to stay organized.

\(P=(6+7)+(4+3)+(1+2)+(3+2)\)

\(P=13+7+3+5\)

\(P=20+3+5\)

\(P=23+5\)

\(P=28\)

Since no inches, centimeters, or feet were given, write the answer in units.

\(\boxed{P=28\text{ units}}\)

🧠 Math Vocabulary

• Perimeter: The total distance around the outside of a figure.
• Irregular shape: A shape whose side lengths are not all the same.
• Boundary: The outside edge of a figure.
• Grid: A set of horizontal and vertical lines used to help measure and draw shapes.
• Units: A general measurement label used when no specific unit is given.

💡 Main Idea

To find the perimeter of an irregular shape on a grid, count the length of each outside side and add them together. Staying organized and moving around the figure in one direction helps make sure every side is included exactly once.

📚 What You Should Already Know

Before this lesson, students should know how to count grid units and add several whole numbers. It also helps to understand that perimeter only uses the outside edge of a shape, not the area inside it.

🚀 What Comes Next

After working with irregular shapes on a grid, students can move on to irregular figures with labeled side lengths, mixed-number dimensions, and perimeter word problems involving real-world situations.

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