WebQuest · Unit 5 · CCSS 6.G.A.1

📐 The Area Architect WebQuest

Area of Polygons — measure, build, and prove every shape!

🎯 Learning Target

I can find the area of a parallelogram using A = b × h.
I can find the area of a triangle using A = ½ × b × h.
I can find the area of a trapezoid using A = ½ × (b₁ + b₂) × h.
I can find the area of a composite figure by splitting it into simpler shapes and adding the parts.

📌 Standard: CCSS 6.G.A.1 ⏱ Estimated time: 45–60 min 📎 Materials: pencil, graph paper (optional), calculator (optional)

TEACHER ONLY — Does not print

Teacher Notes

Pacing

45 min class: Steps 1–3 (~15 min) → Self-Check (~10 min) → Steps 4–5 + Final Quiz (~20 min). 60 min class: add pair-share after each formula step and debrief the composite figure with the whole group.

Grouping

Best used in pairs for Steps 1–4 so students can talk through the cutting strategy for composite figures. Step 5 (final quiz) should be completed individually.

Differentiation — Support

Pre-cut graph-paper shapes so students can physically lay unit squares inside each polygon.
Provide a formula card students can keep visible during the quiz.
Allow students to draw the shape and label base and height before calculating.

Differentiation — Challenge

Ask students to derive the triangle formula from a rectangle (fold/cut proof).
Pose: "Can two different-shaped triangles have the same area? Show an example."
Extend to irregular polygons with more than two composite pieces.

ESOL / Language Supports

Post a visual word wall: base, height, parallelogram, trapezoid, composite with labeled diagrams.
Use sentence frames: "The area is ___ because I used the formula ___."
Allow native-language scratch work; assess the math, not the language.

1. Introduction

Welcome, Area Architect! 🏗️ A new park needs floor plans, and you are the math behind the build.

Area is the number of unit squares that fit inside a flat shape. We measure it in square units (like cm² or ft²). In this WebQuest you will find the area of parallelograms, triangles, trapezoids, and composite figures (shapes made of smaller shapes).

2. Task

By the end, you will be able to:

Find the area of a parallelogram (base × height).
Find the area of a triangle (½ × base × height).
Find the area of a trapezoid (½ × (b₁ + b₂) × height).
Find the area of a composite figure by splitting it into simpler shapes and adding the parts.
Solve a real floor-plan problem and finish the self-check and quiz below.

3. Process

Do the steps in order. Read each one carefully.

Step 1 — Learn the words

Area = space inside a flat shape. Base and height must meet at a right angle (a square corner). For a parallelogram the height is the perpendicular distance between the two bases — not the slanted side.
Step 2 — Learn the formulas

Parallelogram: A = b × h

Triangle: A = ½ × b × h

Trapezoid: A = ½ × (b₁ + b₂) × h

Composite: split into known shapes, find each area, then add
Step 3 — Play the 3D game

Open the Area Architect 3D game. Build blocks to match the gold target area. Watch how base × height fills the parallelogram.
Step 4 — Try a composite figure

An L-shaped room splits into two rectangles (rectangles are special parallelograms). Find each area, then add them together.
Step 5 — Show what you know

Complete the Self-Check below, then type your name in the bar above, finish the final quiz, and Save as PDF or DOC to turn in.

💡 Tip: A triangle is exactly half of a parallelogram with the same base and height. That is why we multiply by ½.

4. Resources

Use these to help you:

🎮 Unit 5 — Area Architect 3D Game — build shapes to a target area.
📘 Math Lessons Hub — review area of polygons.
📖 Unit 5 Graphic Novel — the area story.
📝 Unit 5 Practice Activities — extra practice.

5. Self-Check — Try It Yourself

Answer each question, then press Check to see if you are right. Read the explanation before moving on.

SC1. A parallelogram has a base of 7 cm and a height of 4 cm. What is its area?

Use A = b × h. Type a number.

SC2. A triangle has a base of 10 m and a height of 6 m. What is its area?

Use A = ½ × b × h. Type a number.

SC3. A trapezoid has bases of 5 ft and 9 ft and a height of 4 ft. What is its area?

Use A = ½ × (b₁ + b₂) × h. Type a number.

SC4. An L-shaped floor is made of two rectangles: one is 6 m × 3 m and the other is 4 m × 2 m. What is the total area?

Find each rectangle's area, then add. Type a number.

6. Evaluation (Rubric)

Skill	4 — Expert	3 — Good	2 — Getting there	1 — Keep trying
Parallelogram & rectangle area	Applies A = b × h correctly every time, including slanted sides.	Applies A = b × h correctly most of the time.	Uses the formula with occasional errors.	Needs support to use the formula.
Triangle area	Uses A = ½bh quickly and correctly every time.	Uses the triangle formula correctly.	Uses the formula with help or minor errors.	Triangle area formula not yet mastered.
Trapezoid area	Identifies both bases and height, applies formula correctly every time.	Applies the trapezoid formula correctly.	Applies the formula with prompting.	Has difficulty identifying the two bases.
Composite figures	Splits any composite figure and adds parts with no errors.	Splits and adds parts with few errors.	Finds some parts correctly with guidance.	Cannot yet split the shape independently.

7. Conclusion

Great work, Area Architect! You can now find the area of parallelograms, triangles, trapezoids, and composite figures. These same skills help you plan rooms, gardens, sports fields, and floor plans. Complete the reflection and final quiz below to show what you learned.

8. Reflection

Answer these two questions in your own words before you submit.

1. Which shape was hardest for you — parallelogram, triangle, or trapezoid? Why?

2. Describe one real-life situation where you would need to calculate area.

Deliverable: When you finish the quiz below, press Save as PDF or Save as DOC in the panel at the top of the page, then submit the file to your teacher. Your file should include your name, all quiz answers, and your reflection.

9. Check Your Understanding

Answer all 6. Then press Check My Answers. Type numbers only when asked.

Q1. A parallelogram has a base of 8 cm and a height of 5 cm. What is its area in square cm? Use A = b × h. Example answer: 12

Q2. A triangle has a base of 10 cm and a height of 4 cm. What is its area in square cm? Use A = ½ × b × h. Example answer: 6

Q3. A square garden has sides of 6 ft. What is its area in square ft? A square is a special parallelogram. Example answer: 25

Q4. An L-shaped room is made of two rectangles. One is 12 m², the other is 8 m². What is the total area? Add the parts. Example answer: 30

Q5. Which unit do we use to measure area?

Q6. A trapezoid has bases of 6 in and 10 in and a height of 4 in. What is its area in square inches? Use A = ½ × (b₁ + b₂) × h. Example answer: 24

Your score and a ✓/✗ for each question will appear in the panel at the top. Then use Save as PDF or Save as DOC to turn it in.

Teacher Answer Key (click to expand)

Share with students only after submission. Keep collapsed during student work time.

Item	Correct Answer	Formula / Work
SC1	28 cm²	b × h = 7 × 4 = 28
SC2	30 m²	½ × 10 × 6 = 30
SC3	28 ft²	½ × (5+9) × 4 = ½ × 14 × 4 = 28
SC4	26 m²	6×3 + 4×2 = 18 + 8 = 26
Q1	40 cm²	8 × 5 = 40
Q2	20 cm²	½ × 10 × 4 = 20
Q3	36 ft²	6 × 6 = 36
Q4	20 m²	12 + 8 = 20
Q5	square units	Area is always in square units
Q6	32 in²	½ × (6+10) × 4 = ½ × 16 × 4 = 32

🎯 Learning Target

Teacher Notes

Pacing

Grouping

Differentiation — Support

Differentiation — Challenge

ESOL / Language Supports

1. Introduction

2. Task

3. Process

Step 1 — Learn the words

Step 2 — Learn the formulas

Step 3 — Play the 3D game

Step 4 — Try a composite figure

Step 5 — Show what you know

4. Resources

5. Self-Check — Try It Yourself

6. Evaluation (Rubric)

7. Conclusion

8. Reflection

9. Check Your Understanding