Perimeter of Polygons
Finding the Perimeter of a Rectangle
A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?
Identify the sides: Length = 8 cm, Width = 5 cm = Two sides of 8 cm, two sides of 5 cm
Add all sides: $P = 8 + 5 + 8 + 5$ = $P = 26$ cm
Or use the formula: $P = 2(l + w) = 2(8 + 5) = 2(13)$ = $P = 26$ cm
Answer: The perimeter is 26 cm.
Finding the Perimeter of a Triangle
A triangle has sides of 7 m, 9 m, and 12 m. What is its perimeter?
List all three sides: Side 1 = 7 m, Side 2 = 9 m, Side 3 = 12 m = Three different sides
Add all sides together: $P = 7 + 9 + 12$ = $P = 28$ m
Answer: The perimeter is 28 m.
Regular Hexagon Perimeter
A regular hexagon has sides of 4 cm each. Find its perimeter.
Identify the shape: Hexagon = 6 sides, all equal (regular) = 6 sides of 4 cm
Multiply side by number of sides: $P = 6 \times 4$ = $P = 24$ cm
Answer: The perimeter is 24 cm.
Finding a Missing Side
A rectangle has a perimeter of 30 m and a length of 9 m. What is its width?
Write the formula: $P = 2l + 2w$ = $30 = 2(9) + 2w$
Simplify: $30 = 18 + 2w$ = Subtract 18 from both sides
Solve for width: $12 = 2w$, so $w = 6$ = Width = 6 m
Answer: The width is 6 m.
Mistake: Only adding two sides of a rectangle
Why: A rectangle has four sides, not two. Students sometimes add just length + width instead of all four sides.
Correct: Remember: a rectangle has 2 lengths AND 2 widths. Use $P = 2l + 2w$ or add all four sides.
Mistake: Confusing perimeter with area
Why: Area measures the space inside; perimeter measures the distance around.
Correct: Perimeter is like walking around the edge. Area is like covering the floor with tiles.
Mistake: Forgetting units in the answer
Why: Perimeter is a length measurement and needs units (cm, m, ft, etc.).
Correct: Always include units! If sides are in meters, the perimeter is in meters.
Fencing a Garden
Gardeners calculate perimeter to know how much fencing to buy.
A rectangular garden is 12 m long and 8 m wide. You need $P = 2(12 + 8) = 40$ m of fencing.
Picture Framing
Frame makers need to know the perimeter to cut the right amount of wood or metal.
A photo is 20 cm by 25 cm. The frame needs $P = 2(20 + 25) = 90$ cm of wood.
Running Track
Runners need to know the perimeter to track their distance.
A rectangular field is 100 m by 60 m. One lap is $P = 2(100 + 60) = 320$ m.
Perimeter is the total distance around a polygon
Add all sides together: $P = s_1 + s_2 + s_3 + \cdots$
Rectangle: $P = 2l + 2w$ or $P = 2(l + w)$
Regular polygon: $P = n \times s$ (number of sides times side length)
Always include units in your answer
Q: What's the difference between perimeter and area?
A: Perimeter measures the distance around a shape (like a fence). Area measures the space inside a shape (like carpet covering a floor). Perimeter is measured in units (m, cm). Area is measured in square units (m², cm²).
Q: Can a shape have the same perimeter but different area?
A: Yes! A 1×8 rectangle and a 3×6 rectangle both have perimeter 18, but different areas (8 vs 18 square units).
Q: Does a circle have a perimeter?
A: Yes, but we call it the circumference. It's calculated differently using $C = 2\pi r$ or $C = \pi d$.
Perimeter of Polygons
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Perimeter of Polygons
Learn how to calculate the distance around any polygon by adding up all its sides.