Area and Perimeter of Composite Figures

Hands-on activities allow students to physically manipulate shapes, which helps them see how composite figures break apart into familiar components. This tactile approach builds intuition about area and perimeter in ways worksheets alone cannot replicate.

• Primary 4
• Mathematics
• 4 activities
• 30 min–45 min

Learning Objectives

1. Calculate the area of composite figures by decomposing them into rectangles, triangles, and parallelograms.
2. Determine the perimeter of composite figures by identifying and summing only the exterior sides.
3. Compare the methods for finding the area and perimeter of simple shapes versus composite figures.
4. Analyze composite figures to identify the component shapes and their dimensions.
5. Explain the strategy used to find the area and perimeter of a given composite figure.

Collaborative Problem-Solving

⏱ 35 min·Pairs

Geoboard Builds: Composite Creations

Supply geoboards, rubber bands, and grid paper. Students construct composite figures with two or three basic shapes, sketch the outline, then compute area by counting squares and perimeter by measuring edges. Pairs swap shapes to verify each other's work.

Prepare & details

How do you read information from a table or a bar graph to answer questions?

Facilitation Tip: During Geoboard Builds, have students describe their shape’s decomposition to a partner before measuring to reinforce verbal reasoning alongside visual work.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 40 min·Small Groups

Paper Cutouts: Decompose and Measure

Provide grid paper templates of L-shapes or T-shapes. Students cut along decomposition lines into rectangles and triangles, label dimensions, calculate individual areas and total perimeter. Small groups reassemble and present findings.

Prepare & details

What does the scale on a bar graph mean, and how do you use it to read values accurately?

Facilitation Tip: When students do Paper Cutouts, collect leftover scraps and ask them to prove their total area matches the original shape’s dimensions.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 30 min·Small Groups

String Trace: Perimeter Hunt

Draw composite figures on large chart paper. Groups use string to trace outer perimeters, measure lengths, and compare to calculated values. Extend by designing their own shapes for classmates to solve.

Prepare & details

Can you collect data, organise it in a table, and then draw a bar graph to display it?

Facilitation Tip: For String Trace, challenge groups to find the shortest possible perimeter path by adjusting their figure’s shape slightly.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 45 min·Whole Class

Grid Puzzle: Area Challenges

Distribute puzzles where students fill grids to form composites matching given areas. They record decompositions and perimeters. Whole class shares strategies via gallery walk.

Prepare & details

How do you read information from a table or a bar graph to answer questions?

Facilitation Tip: In Grid Puzzle, require students to trade solutions with another group and verify each other’s calculations before moving on.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Start with concrete manipulatives like geoboards or paper shapes to establish the concept of breaking apart figures. Move to grid-based activities to reinforce decomposition and measurement, avoiding abstract formulas until students can explain why they add or ignore certain sides. Research shows students who draw decomposition lines before calculating make fewer errors in perimeter and area.

What to Expect

Students should confidently decompose composite figures into simpler shapes, apply area and perimeter formulas correctly, and justify their calculations by labeling dimensions. Peer collaboration ensures they internalize these steps through discussion and verification.

Watch Out for These Misconceptions

Common Misconception

During String Trace, watch for students who include internal edges when measuring perimeter with string.

What to Teach Instead

Have students lay the string only along the outer edge and mark where it meets itself to show that internal sides do not count. Ask them to compare their string length to the sum of all sides to highlight the difference.

Common Misconception

During Paper Cutouts, watch for students who skip breaking the composite figure into parts before measuring area.

What to Teach Instead

Prompt them to rearrange the cut pieces into a single shape they can measure easily, like a rectangle, to demonstrate why summing parts works better than guessing.

Common Misconception

During Geoboard Builds, watch for students who use the triangle’s base and height incorrectly after combining it with other shapes.

What to Teach Instead

Ask them to test different base-height pairs on the geoboard to see which combination matches the figure’s actual dimensions, then discuss why only one pair is valid for area calculation.

Assessment Ideas

Quick Check

After Geoboard Builds and Paper Cutouts, provide a worksheet of composite figures. Ask students to decompose each figure by drawing lines, label dimensions, and calculate area and perimeter, using the same steps they practiced in the activities.

Exit Ticket

After String Trace, give each student a composite figure with all dimensions labeled except one side. Ask them to write the steps to find the missing side, then calculate the total perimeter, showing their work with the decomposition lines they used during the activity.

Discussion Prompt

During Grid Puzzle, present two different decomposition methods for the same figure. Ask students to discuss in pairs which method they prefer and why, focusing on accuracy and ease of calculation. Circulate to listen for clear justifications about avoiding overlap or missing parts.

Extensions & Scaffolding

• Challenge: Provide a composite figure with a missing dimension. Students must solve for the missing side before calculating area or perimeter.
• Scaffolding: Offer predrawn decomposition lines on grid paper for students to measure parts directly.
• Deeper: Ask students to design their own composite figures with specific area and perimeter constraints, then trade designs with peers to solve.

Key Vocabulary

Composite Figure	A shape made up of two or more simpler geometric shapes, such as rectangles, triangles, or parallelograms.
Decomposition	The process of breaking down a complex shape into smaller, familiar shapes to make calculations easier.
Exterior Sides	The boundary lines of a composite figure that are on the outside edge; internal lines are not included in the perimeter.
Area	The amount of two-dimensional space a shape covers, measured in square units.
Perimeter	The total distance around the outside edge of a shape, measured in linear units.