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Area of Triangles & Parallelograms

Sixth graders find the area of parallelograms (base × height) and triangles (half of that) — discovering why a triangle is exactly half a parallelogram, and why the height must be the straight-up distance.

Grade 6Area50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Find the area of a parallelogram.
  • ✓Find the area of a triangle.
  • ✓Use the correct height.
  • ✓Explain the ½ in the triangle formula.
Essential Question

A parallelogram’s area is base × height — but which measurement is the “height”? And why does a triangle’s area have a ½ in it?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

Area Explorer

Project this and switch between a parallelogram and a triangle. Change the base and height, and watch the area formula work!

📐 Explore the area of triangles & parallelogramsTry it
Base: 6
Height: 4

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Which Is the Height?

5 min

A parallelogram’s area is base × height — but which line is the height?

👩‍🏫 Teacher Moves

  • Show a parallelogram.
  • Ask which is the height.
  • Set the goal: area.

🎒 Student Actions

  • Look at the shape.
  • Guess the height.
  • Predict the idea.
2

I Do — Base × Height

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Parallelogram: base × height.
  • Triangle: half of that.
  • Height is straight up.

🎒 Student Actions

  • Learn parallelogram.
  • Learn triangle.
  • Find the height.
3

We Do — Explore Together

13 min

Class uses Area Explorer.

👩‍🏫 Teacher Moves

  • Switch shapes.
  • Change base and height.
  • Read the area.

🎒 Student Actions

  • Switch shapes.
  • Set values.
  • Read area.
4

You Do — On Your Own

12 min

Students find area.

👩‍🏫 Teacher Moves

  • Find parallelogram areas.
  • Find triangle areas.
  • Use the right height.

🎒 Student Actions

  • Find areas.
  • Use height.
  • Solve them.
5

Close — Close

5 min

One shape.

👩‍🏫 Teacher Moves

  • Give a shape with measurements.
  • Find its area.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find the area.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
6.G.1

Find the area of triangles, quadrilaterals, and polygons.

CCSS
6.G.1

Compose and decompose shapes to find area.

CCSS
6.EE.2

Evaluate area formulas.

SMP
MP.4

Model area with drawings and formulas.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Label base and height.
  • Sentence frame: “Area = base × height = ___.”
  • Cut a parallelogram into a rectangle.

Support & Access

IEP / 504
  • Start with parallelograms.
  • Use grid paper to count.
  • Highlight the height.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find the area of composite shapes.
  • Find a missing base or height.
  • Find the area of trapezoids.
Materials

What to gather

  • 📽️Projector / board
  • 📐Grid paper
  • 💻Area Explorer
  • ✂️Paper shapes
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

areathe space inside a shapebasea side used to measureheightthe straight-up distance to the baseparallelograma quadrilateral with parallel sidestrianglea three-sided polygonsquare unitsthe units for areaformulaa rule for calculatingdecomposeto break into parts
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is the area of a parallelogram with base 8 and height 5?
40 square units (8 × 5).
QUESTION 2
What is the area of a triangle with base 6 and height 4?
12 square units (½ × 6 × 4).
QUESTION 3
Why does the triangle area formula have a ½ in it?
Because a triangle is exactly half of a parallelogram with the same base and height.

Going deeper? Composite shapes.

Have students find the area of composite figures by breaking them into triangles and parallelograms. A printable area sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Area of Triangles & ParallelogramsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Area of Triangles & ParallelogramsQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Area of Triangles & ParallelogramsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: area, base, decompose, formula, height, parallelogram, square units, triangle
  1. the straight-up distance to the base
  2. to break into parts
  3. the units for area
  4. a quadrilateral with parallel sides
  5. a three-sided polygon
  6. a side used to measure
  7. the space inside a shape
  8. a rule for calculating

Part B · Show what you learned

  1. What is the area of a parallelogram with base 8 and height 5?
  2. What is the area of a triangle with base 6 and height 4?
  3. Why does the triangle area formula have a ½ in it?
Answer key — Part A: 1) height · 2) decompose · 3) square units · 4) parallelogram · 5) triangle · 6) base · 7) area · 8) formula
Part B: 1) 40 square units (8 × 5). 2) 12 square units (½ × 6 × 4). 3) Because a triangle is exactly half of a parallelogram with the same base and height.