Welcome to Add Side Lengths Strategically! This second lesson focuses on finding the perimeter of triangles and irregular polygons. Triangles and irregular shapes show up in many everyday measurements, from triangular garden plots to oddly shaped patios with six or seven edges. Because their sides do not always come in matching sets, you cannot rely on a single tidy formula. Instead, you will learn to identify every outer edge and add the side lengths strategically.

In this lesson, you will learn to:

• Calculate the perimeter of different types of triangles and irregular polygons.
• Add whole-number and decimal side lengths accurately.
• Trace boundaries systematically to ensure no outer edge is missed or counted twice.

The shortcuts you learned for squares ($P = 4 \times s$) and rectangles ($P = 2 \times (l + w)$) both rely on the fact that certain sides are guaranteed to be equal. When that guarantee disappears, the shortcuts disappear too.

A triangle has exactly three sides. No matter what the triangle looks like, its perimeter is always:

Here $a$, $b$, and $c$ represent the three side lengths. The three common triangle types each offer a slightly different summing experience:

Real-world triangles rarely have perfectly round measurements. A triangular garden plot might have sides of $5.4\text{ m}$, $3.8\text{ m}$, and $6.1\text{ m}$. The formula does not change. You just need to be more careful with the addition.

Example: Find the perimeter of a triangle with sides $5.4\text{ m}$, $3.8\text{ m}$, and .

An irregular polygon is any polygon that is not regular — that is, its sides are not all equal, or its angles are not all equal, or both. Think of the floor plan of an L-shaped room or the outline of a yard that is not a simple rectangle. These shapes can have four, five, six, or more sides, and our approach stays the same — just with more terms to track:

With squares and rectangles, the structure of the formula kept you on track. With irregular shapes, there is more room for error. Two pitfalls come up again and again:

1. Skipping a side. When a shape has many edges or an unusual layout, it is easy to overlook one. Always count the total number of sides first and verify that your addition has the same number of terms.
2. Counting a side twice. When tracing a boundary, you might accidentally revisit an edge you already recorded, especially at corners where two sides meet. Mark or check off each side as you go to avoid duplicates.

A practical habit is to start at one corner and move consistently in one direction, either clockwise or counterclockwise, listing each side in order. This organized tracing makes it much harder to skip or double-count an edge.

Here is a compact summary of everything covered in this lesson:

In this lesson, you moved beyond the neat formulas for squares and rectangles and learned to find the perimeter of triangles and irregular polygons by summing all boundary sides. For triangles, small shortcuts exist when sides repeat (equilateral and isosceles), but the core method is always $P = a + b + c$. For irregular polygons, the same idea extends to as many sides as the shape has — the key is counting every edge exactly once.

Now it is time to put these skills to work! In the practice section ahead, you will identify which segments belong to a shape's boundary, trace perimeters interactively, calculate side sums for various triangles and polygons with whole-number and decimal lengths, and spot errors in someone else's calculation. Let's see how sharp your perimeter skills have become.