MathIsimple
Unit 4: Lesson 3

Perimeter of Rectangles & Composite Figures

Measure every edge! Learn how to find the distance around rectangles and combined shapes. Walk the perimeter, add the sides, and master real-world measurement problems. 🚶📏

40-45 min
Medium
Perimeter Formula
Composite Shapes
Missing Side Lengths
Real-World Measurement

🎯 Interactive Perimeter Practice

Master perimeter by exploring interactive measurement challenges!

Rectangle Perimeter Warm-Up

Review the perimeter formula for rectangles!

Easy
6 minutes
🪜

📐 A rectangle is 12 meters long and 8 meters wide. What is its perimeter?

m
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Identify Correct Strategy

Choose the best approach to find perimeter!

Medium
7 minutes
🧮

🧠 Which method will ALWAYS find the perimeter of any shape?

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Missing Side Detective

Find missing sides using perimeter clues!

Medium
8 minutes
🗝️

🕵️ Arrange the steps to solve: A rectangle has perimeter 54 cm and width 12 cm. Find the length!

Drag to sort or use ↑↓ buttons to adjust · Correct Order

1
Calculate: Length = 15 cm
2
📐Use perimeter formula: 2 × (Length + Width) = 54
3
Subtract the known width: Length = 27 - 12
4
Divide both sides by 2: Length + Width = 27
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Composite Figure Challenge

Calculate the perimeter of combined rectangles!

Hard
9 minutes
🌿

🧩 An L-shaped garden is made from two rectangles: one 6m × 4m and one 4m × 3m sharing a side. Which steps correctly find its perimeter?

Click all correct options

Selected: 0
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📚 Master Perimeter Concepts

Understand perimeter deeply through examples, visuals, and real-world connections

What Is Perimeter?

Perimeter is all about edges! It's the sum of every side length of a shape. Use it when you need to enclose something or measure a path. Remember: perimeter measures distance, not area!

🌟Examples:

👟

Walk the Border

Perimeter is the distance around a shape. Imagine walking around a playground—your total steps equal the perimeter. It's the boundary length! 🚶

🪵

Fence Builder

Need to build a fence around a garden? Measure each side, add them up—that total is the perimeter. Helps you buy the right amount of fencing! 🌱

🖼️

Perimeter vs. Area

Perimeter measures edges; area measures space inside. You could use perimeter to frame a picture, area to cover a wall. Different jobs! 🎨

📐

Units Stay Linear

Perimeter uses regular units: cm, m, ft. They never become squared because you're measuring length, not coverage! 📏

Pro Tip! 💡

Trace your finger along the shape. Each segment you touch gets added to the perimeter!

Common Mistake Alert! ⚠️

Mixing up area and perimeter. If the question asks about boundary, think perimeter!

Real-World Use 🌍

Fencing yards, framing art, outlining sports fields, installing trim—perimeter is essential!

Practice Idea! 🎯

Take string and lay it around different objects. Measure the string to find perimeter!

Rectangle Perimeter Formula

Rectangles are the only shapes with opposite sides equal. This symmetry gives us the handy formula: Perimeter = 2(L + W). Memorize it, and you can find rectangle perimeters quickly!

🌟Examples:

🔢

Standard Formula

For any rectangle: Perimeter = 2 × (Length + Width). Because opposite sides are equal! Add length and width, double the sum. Efficient and fast! 🧮

📏

Example

Rectangle 9m × 5m: P = 2 × (9 + 5) = 2 × 14 = 28m. Or add sides individually: 9 + 5 + 9 + 5 = 28. Same outcome! 📐

🟥

Square Special Case

Squares are rectangles with equal sides. If side = 8cm, Perimeter = 4 × side = 32cm. Still the same formula—just easier! ▢

✔️

Check Your Work

After calculating, mentally add sides to confirm! If you get the same sum by counting each side, your formula usage is correct. Double-checks build confidence! ✅

Pro Tip! 💡

Write the formula down before plugging in numbers. It keeps your thinking clear and organized!

Common Mistake Alert! ⚠️

Multiplying length and width instead of adding first. Remember: perimeter adds sides, area multiplies!

Real-World Use 🌍

Planning picture frames, laying baseboards, wrapping packages—rectangles are everywhere!

Practice Idea! 🎯

Create flash cards with random lengths & widths. Challenge yourself to calculate perimeter quickly!

Perimeter of Composite Shapes

Composite shapes look tricky, but the strategy stays simple: trace the outline, label every outer side, find missing lengths, then add them all. It's like walking around the shape—just keep moving forward and count each side once!

🌟Examples:

🖊️

Outline the Shape

Composite shapes combine rectangles (like L-shapes). Trace the outer edge. Only add the sides that outline the shape—ignore internal lines! 🧩

Shared Sides

If two rectangles share a side, that edge is inside the shape. Don't include it in the perimeter! Only outer boundaries count! 🚫

📏

Label Missing Lengths

Use subtraction to find missing side lengths. Example: Total horizontal = 12m, small section = 4m, so remaining side = 8m. Fill in the gaps first! 📐

🔄

Add Carefully

Once all sides are known, add them systematically (clockwise or counterclockwise). Check you included each outer side exactly once! ✅

Pro Tip! 💡

Color-code outer edges when drawing. It makes it easier to see which sides to add!

Common Mistake Alert! ⚠️

Accidentally adding interior lines or skipping a small edge. Go slowly and check your path.

Real-World Use 🌍

Designing patios, building decks, creating park paths—real structures often combine rectangles!

Practice Idea! 🎯

Cut paper rectangles and tape them into L-shapes. Measure each side yourself to build intuition!

Perimeter vs. Area

Area and perimeter behave differently. You can't predict one from the other. Always read the question to know which to compute. Train yourself to spot keywords so you choose the right formula!

🌟Examples:

⚖️

Different Questions

Area asks: How much space is covered? Perimeter asks: How far around? Example: Painting = area, fence = perimeter. Know what you're solving! 🎨 vs. 🪵

📊

Same Perimeter, Different Area

Rectangle 12×2 has perimeter 28 and area 24. Rectangle 7×7 has perimeter 28 but area 49. Same perimeter ≠ same area! 🤯

🔁

Same Area, Different Perimeter

Rectangles 8×6 and 12×4 both have area 48. Perimeters: 28 vs. 32. Same area ≠ same perimeter! Shapes matter. 📐

🧠

Choose Carefully

Read word problems slowly. Keywords: fence, border, frame → perimeter. Cover, surface, tile → area. The clue tells you which measurement! 🔍

Pro Tip! 💡

Underline keywords in word problems: 'around,' 'border,' 'fence' = perimeter. 'Cover,' 'paint,' 'fill' = area.

Common Mistake Alert! ⚠️

Using the wrong formula due to rushing. Slow down and identify the question first!

Real-World Use 🌍

Buying flooring vs. trim, landscaping (mulch vs. fencing), building frames vs. panels.

Practice Idea! 🎯

Create scenarios and decide: area or perimeter? Explain why before solving!

Finding Missing Side Lengths

Missing sides aren't missing forever! Use known lengths and the perimeter formula to uncover them. Subtract, divide, and always verify. Turn measurement problems into satisfying detective work!

🌟Examples:

📏

Rectangles

If perimeter is known, use 2(L + W) to find the missing side. Example: P = 50, W = 8 → 2(L + 8) = 50 → L + 8 = 25 → L = 17. Works every time! 🧠

✂️

Composite Shapes

Use total lengths: If total top edge is 18 and part is 5, the remainder is 13. Subtract known segments to uncover missing sides. 🔍

🟥

Squares

If perimeter of a square is 48 cm, each side is 48 ÷ 4 = 12 cm. Squares make it easy—just divide by 4! ▢

✔️

Check by Addition

After solving, add all sides to check if they match the given perimeter. Verification catches mistakes! ✅

Pro Tip! 💡

Draw diagrams with all known measurements labeled. The visual makes missing sides obvious!

Common Mistake Alert! ⚠️

Forgetting to subtract both parallel segments in composite shapes. Always consider the shape's symmetry!

Real-World Use 🌍

Designing floor plans, quilting patterns, building frames—missing measurements happen often!

Practice Idea! 🎯

Create your own rectangle problems. Give perimeter and one side, solve for the other!

Real-World Perimeter Applications

Perimeter isn't abstract—it solves everyday problems! From fencing to flooring to crafting, knowing perimeter saves time and money. Make perimeter your go-to tool whenever you're working with edges and borders!

🌟Examples:

🌳

Gardening

Putting a fence around a rectangular garden? Measure length and width, then calculate perimeter to buy enough fencing. No guesswork needed! 🌼

🪚

Home Improvement

Installing baseboards around a room? Use perimeter to know how many feet of trim to buy. Saves extra trips to the hardware store! 🏠

🏟️

Sports Fields

Marking track lanes or soccer fields uses perimeter to determine boundary line lengths. Sports engineers rely on it! ⚽

🧶

Crafts & Sewing

Need ribbon to edge a blanket? Measure each side and add them up. Perimeter ensures you have the right amount before cutting! 🧵

Pro Tip! 💡

Before purchasing materials, calculate perimeter and add 5-10% extra for mistakes or overlaps!

Common Mistake Alert! ⚠️

Eyeballing measurements. Always measure precisely and calculate correctly to avoid shortages!

Real-World Use 🌍

Construction, landscaping, athletics, crafting, shipping, fashion design—perimeter is everywhere!

Practice Idea! 🎯

Plan a mini project: 'How much tape to outline this poster?' Measure and calculate before cutting!