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NN.2 Perimeter with side lengths

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What is perimeter?

Perimeter is the total distance around the outside of a two-dimensional shape. Think of it as the length of the boundary that encloses the shape.

Real-World Example:
  • The distance you would walk around a soccer field
  • The length of fencing needed to enclose a backyard
  • The border around a picture frame
Remember

Perimeter is always measured in linear units like inches, feet, yards, centimeters, or meters.

Finding perimeter of polygons

To find the perimeter of any polygon, add the lengths of all its sides together.

Formula:

Perimeter = side + side + side + ... (add all sides)

Examples:
  • Triangle with sides 5 cm, 7 cm, 9 cm → Perimeter = 5 + 7 + 9 = 21 cm
  • Rectangle with sides 8 ft and 12 ft → Perimeter = 8 + 12 + 8 + 12 = 40 ft
  • Pentagon with equal sides of 6 m → Perimeter = 6 + 6 + 6 + 6 + 6 = 30 m
Strategy

When solving perimeter problems, first identify all side lengths, then add them carefully. Double-check your addition.

Special cases regular polygons

A regular polygon has all sides equal in length and all angles equal in measure.

Shortcut Formula:

Perimeter = number of sides × length of one side

Examples:
  • Square with side 5 in → Perimeter = 4 × 5 = 20 inches
  • Regular hexagon with side 7 cm → Perimeter = 6 × 7 = 42 centimeters
  • Equilateral triangle with side 9 ft → Perimeter = 3 × 9 = 27 feet
Remember

This shortcut only works for regular polygons where all sides are exactly the same length.

Finding missing side lengths

Sometimes you know the perimeter but need to find a missing side length. Use the total perimeter and the known sides to calculate the unknown measurement.

Examples:
  • Perimeter = 34 units, three sides = 8, 12, and 7 units
    Missing side = 34 - (8 + 12 + 7) = 34 - 27 = 7 units
  • Rectangle perimeter = 28 m, length = 9 m
    Width = (28 - 2×9) ÷ 2 = (28 - 18) ÷ 2 = 10 ÷ 2 = 5 meters
Strategy

For rectangles: Perimeter = 2 × length + 2 × width. If you know perimeter and one dimension, you can find the other.

Perimeter of complex shapes

Some shapes have sides of different lengths or may be composed of multiple rectangles. To find the perimeter, still add all the outside edge lengths.

Examples:
  • L-shaped figure: Add all outside edges, don't count the interior line where two rectangles join
  • U-shaped garden: Measure only the outer boundary, not the interior pathways
  • House floor plan: Follow the outside walls only
Important

When finding perimeter of complex shapes, trace the outside boundary with your finger to ensure you include all outside edges and exclude interior lines.

Perimeter in real world problems

Understanding perimeter helps solve practical problems in construction, gardening, sports, and everyday life.

Application Examples:
  • How much trim is needed for a bulletin board?
  • How much fencing is required for a pet enclosure?
  • What length of ribbon is needed to outline a poster?
  • How far will you run if you go around the track once?
Problem-Solving Tip

When solving real-world perimeter problems, always include units in your final answer and make sure they make sense for the situation.

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