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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.
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Interactive Vocabulary

Reveal one step at a time

Worked Examples

Example 1

Parallelogram b=12,h=5

1

A=bh=60 square units.

Example 2

Trapezoid b₁=6,b₂=10,h=4

1

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.

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Area of Polygons lesson and examples

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Warm-Up Guided Independent Challenge
1
Quick Start

Warm-Up

Warm-up 1

Directions: Solve the problem. Show your thinking, then enter only your final answer.

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

Picture the measurementUse the picture to organize what you know before you solve.
mL

Choose how you want to work or answer.

2
We Do

Guided Practice

3
You Do

Independent Practice

Independent 1

Directions: Solve independently. Show your work, check it, then enter only your final answer.

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

Picture the measurementUse the picture to organize what you know before you solve.
mL

Choose how you want to work or answer.

Independent 2

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Create and solve a second example with different values.

Picture the area and perimeterUse the picture to organize what you know before you solve.
5 units3 units

Choose how you want to work or answer.

4
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.

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Khan Academy

DeltaMath

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