Area of Trapezoids
I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.
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🎯 Content Objective / Objetivo de contenido
I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The trapezoidal window has a top edge of 4 feet and a bottom edge of 8 feet. Why does the area formula use BOTH bases instead of just one?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Blueprint Review
Your architecture firm is designing a trapezoidal window for a modern building. The glass supplier charges by the square foot, so the team must calculate the exact area. The window has a top edge of 4 feet, a bottom edge of 8 feet, and a height of 5 feet.
Concept Launch
💡 How do we find the area of a trapezoid?
A trapezoid is a four-sided shape with one pair of parallel sides. The two parallel sides are called the bases, and they have different lengths.
Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Trapezoid Trapecio |
A four-sided shape with just one pair of parallel sides. Una figura de cuatro lados con solo un par de lados paralelos. |
A table top wider than the bottom shelf — the top and bottom edges are parallel, the two sides slant inward | |
| Base 1 (b1) Base 1 (b1) |
One of the two parallel sides of a trapezoid. Uno de los dos lados paralelos de un trapecio. |
If the bottom of the trapezoid is 10 ft, then b₁ = 10 ft in the formula A = ½(b₁ + b₂) × h | |
| Base 2 (b2) Base 2 (b2) |
The other parallel side of a trapezoid. El otro lado paralelo de un trapecio. |
If the top of the trapezoid is 6 ft, then b₂ = 6 ft; both bases are parallel to each other | |
| Height Altura |
The straight-up distance between the two parallel sides. La distancia recta entre los dos lados paralelos. |
A dashed vertical line from the top base straight down to the bottom base at a 90° angle — NOT the slanted side | |
| Area Área |
How much space is inside a flat shape. Cuánto espacio hay dentro de una figura plana. |
A trapezoid with b₁ = 10, b₂ = 6, h = 4 has area = ½(10 + 6) × 4 = 32 sq units |
Which Word Fits?
A quadrilateral with exactly one pair of parallel sides is a ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
The trapezoidal window has a top edge of 4 feet and a bottom edge of 8 feet. Why does the area formula use BOTH bases instead of just one?
👂 Listen For
Students explain a trapezoid has two parallel sides of different lengths, so using only one would over- or under-count the area; strong answers mention averaging the bases.
Extend: The wonder prompt asks what happens if both bases are equal. Predict the shape and explain how the trapezoid formula would simplify in that case.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Plot the vertices of a trapezoid with bases of 8 and 4, and height of 5. Place points at (0, 0), (8, 0), (6, 5), and (2, 5).
✍️ Explore Discourse
If you copied this trapezoid, flipped it, and placed it next to the original, what shape would you get? How does this help you find the area?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
On the grid you copied the trapezoid (bases 8 and 4, height 5), flipped it, and joined it to the original. What shape formed, and how does that explain the 1/2 in the formula?
👂 Listen For
A strong answer names a parallelogram, links the 1/2 to taking half of two combined trapezoids, and computes area = 1/2 x 12 x 5 = 30 sq ft.
Extend: Compare finding a trapezoid's area to averaging the two bases and multiplying by the height. Are these the same method? Justify with the window numbers.
Practice Check A
What is the area of a trapezoid with bases 6 cm and 10 cm, and height 4 cm?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A trapezoid has an area of 45 sq ft, bases of 7 ft and 11 ft. What is the height?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Area Grid Shading
Click cells to shade area. Count shaded squares.
✍️ Justify Your Thinking
Calculate the area of each trapezoid, then sort by whether the area is greater than 40 sq units or not.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half." — and it works because ___.
Because Trapezoid means ___, but a tricky part is ___, so I have to ___.
A common mistake with Trapezoid is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Base 1 (b1) to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half. because ___
Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half. but ___
Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot the vertices of a trapezoid with bases of 8 and 4, and height of 5. Place points at (0, 0), (8, 0), (6, 5), and (2, 5).
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is the area of a trapezoid with bases 6 cm and 10 cm, and height 4 cm?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A builder is pouring concrete for a trapezoidal driveway. The driveway has parallel edges of 20 feet and 12 feet with a height of 15 feet. One bag of concrete covers 6 square feet.
✍️ Connection Reasoning
How many bags of concrete does the builder need?
The driveway's area is ___ sq ft because A = 1/2 x (___ + ___) x ___. He needs ___ bags because ___ / 6 = ___.
Turn & Talk — Connect
The builder pours concrete for a trapezoidal driveway with edges of 20 ft and 12 ft and a height of 15 ft; one bag covers 6 sq ft. Walk through finding the number of bags.
👂 Listen For
Students compute area = 240 sq ft, then 240 / 6 = 40 bags, and explain why dividing by coverage gives the bag count.
Extend: If the builder doubled only the height of the driveway, would the number of bags double? Justify using the formula.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A trapezoid has bases of 9 inches and 5 inches, and a height of 6 inches. What is its area?
Bonus Exit Check
What is the first step when finding the area of a trapezoid?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students explain a trapezoid has two parallel sides of different lengths, so using only one would over- or under-count the area; strong answers mention averaging the bases.
• A strong answer names a parallelogram, links the 1/2 to taking half of two combined trapezoids, and computes area = 1/2 x 12 x 5 = 30 sq ft.
• Students compute area = 240 sq ft, then 240 / 6 = 40 bags, and explain why dividing by coverage gives the bag count.
• Listen for students naming a specific strategy tied to 6.G.1 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Area of Trapezoids is skipping the key idea: "Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 32 sq cm — A = ½ × (b₁ + b₂) × h = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 sq cm.
✓ Practice 2: 5 ft — A = ½ × (b₁ + b₂) × h → 45 = ½ × 18 × h → 45 = 9h → h = 5 ft.
✓ Practice 3: Add the two bases together — The formula is A = ½ × (b₁ + b₂) × h. The first step is to add the two parallel bases.
✓ Practice 4: 42 sq in — A = ½ × (5 + 9) × 6 = ½ × 14 × 6 = ½ × 84 = 42 sq in.
✓ Exit ticket: 42 sq in — A = 1/2 x (b1 + b2) x h = 1/2 x (9 + 5) x 6 = 1/2 x 14 x 6 = 42 square inches.