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Area of Triangles, Quadrilaterals, and Polygons

Students choose, derive, and apply area formulas for common polygons and irregular figures.

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Beginner 15–20 minutes Volume & Area

Volume & Area Page 2 of 8

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At a Glance

Area of Triangles, Quadrilaterals, and Polygons

Binder SectionVolume & Area

DifficultyBeginner

Estimated Time15–20 minutes

PrerequisitesNone

Essential Question

How can decomposition produce reliable area formulas for polygons?

Build Understanding

Area measures the region inside a two-dimensional figure. Rectangle: A = bh. Triangle: A = one-half bh. Parallelogram: A = bh. Trapezoid: A = one-half(b1 + b2)h.

The height must be perpendicular to the chosen base. For irregular polygons, decompose the figure into familiar shapes, find each area, and add or subtract.

Visual Model

4Thousands 3Hundreds 2Tens 7Ones

4,327 = 4,000 + 300 + 20 + 7

Goals

Learning Targets

Use perpendicular height.
Match the formula to the figure.
Decompose unfamiliar polygons.
Add or subtract component areas.
Use square units.

Click each word

Interactive Vocabulary

Reveal one step at a time

Worked Examples

Example 1

Parallelogram b=12,h=5

A=bh=60 square units.

Example 2

Trapezoid b₁=6,b₂=10,h=4

A=1/2(6+10)(4)=32 square units.

Ask and explain

Common Questions

Is a slanted side always the height? No.

Why is triangle area half of bh? Two matching triangles form a parallelogram.

Can a figure have more than one useful base? Yes.

Notice and correct

Common Misconceptions

Using a slanted side as height

Height must be perpendicular to the base.

Forgetting the one-half factor for triangles or trapezoids

Connect the formula to decomposition.

Learn Through Video

Watch, pause, and explain

Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.

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Now Playing

How to Find Area - Rectangles, Squares, Triangles, and Circles

1 How to Find Area - Rectangles, Squares, Triangles, and Circles 2 Perimeter, Area, and Volume Explained - Math with Mr. J

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Build Your Skills

Practice until you can explain it

Move from a quick warm-up to guided practice, independent work, and deeper challenges.

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Warm-Up Guided Independent Challenge

Quick Start

Warm-Up

Warm-up 1

Find the area of a parallelogram with base 14 and height 6.

We Do

Guided Practice

Guided 1

Triangle b=12, h=7: A=42 square units.

Guided 2

Parallelogram b=9, h=5: A=45.

Guided 3

Trapezoid bases 8 and 14, h=6: A=66.

Guided 4

Rectangle 11 by 4: A=44.

Guided 5

20-by-12 rectangle with 5-by-3 corner removed: A=225.

You Do

Independent Practice

Independent 1

Find the area of a parallelogram with base 14 and height 6.

Independent 2

Create and solve a second example with different values.

Stretch Your Thinking

Challenge & Real-World Practice

🧩 Challenge

Decompose an irregular polygon in two different ways. Prove that both methods give the same total area.

IXL

Area of Triangles

Open resource

IXL

Area of Trapezoids

Open resource

IXL

Area of Compound Figures

Open resource

Khan Academy

Area and Surface Area

Open resource

Khan Academy

Area of Shapes

Open resource

DeltaMath

DeltaMath: Area of Triangles and Quadrilaterals

Open resource

DeltaMath

DeltaMath: Area of Composite Polygons

Open resource

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Success Criteria

Before you begin, I can…

I can identify the important information.
I can use accurate notation, labels, and units.
I can justify and verify my conclusion.

Question 1

What should happen before calculating?

Question 2

Which response gives the strongest evidence?

Question 3

What is an effective accuracy check?

Question 4

Why are units or labels important?

Question 5

What should a student do after finding an error?

Confidence Check

How confident do you feel?

Lesson Complete

Great job on Area of Triangles, Quadrilaterals, and Polygons!

You reviewed the lesson, practiced the skill, and completed the mastery check.

Next Lesson: Area of Circles → Back to Binder Topics

At a Glance

Learning Targets

Interactive Vocabulary

Worked Examples

Parallelogram b=12,h=5

Trapezoid b₁=6,b₂=10,h=4

Common Questions

Common Misconceptions

Watch, pause, and explain

How to Find Area - Rectangles, Squares, Triangles, and Circles

Ready to practice?

Practice until you can explain it

Warm-Up

Find the area of a parallelogram with base 14 and height 6.

Guided Practice

Triangle b=12, h=7: A=42 square units.

Parallelogram b=9, h=5: A=45.

Trapezoid bases 8 and 14, h=6: A=66.

Rectangle 11 by 4: A=44.

20-by-12 rectangle with 5-by-3 corner removed: A=225.

Independent Practice

Find the area of a parallelogram with base 14 and height 6.

Create and solve a second example with different values.

Challenge & Real-World Practice

Nice work!

IXL

Area of Triangles

Area of Trapezoids

Area of Compound Figures

Khan Academy

Area and Surface Area

Area of Shapes

DeltaMath

DeltaMath: Area of Triangles and Quadrilaterals

DeltaMath: Area of Composite Polygons

Save today’s lesson and grow your MathBinder

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Your Binder Achievements

Learned. Watched. Practiced. Saved.

My Math Journal

How confident do you feel?

Complete the thought

What do you want to remember?

My Journal History

Ready to check your understanding?

Can you do this on your own?

Before you begin, I can…

What should happen before calculating?

Which response gives the strongest evidence?

What is an effective accuracy check?

Why are units or labels important?

What should a student do after finding an error?

How confident do you feel?

Your Results

Review and try again

Great job on Area of Triangles, Quadrilaterals, and Polygons!