Unit 5 · Standard 6.G.1
Area of Trapezoids
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
A table top wider than the bottom shelf — the top and bottom edges are parallel, the two sides slant inward
Trapezoid
A four-sided shape with just one pair of parallel sides.
If the bottom of the trapezoid is 10 ft, then b₁ = 10 ft in the formula A = ½(b₁ + b₂) × h
Base 1 (b1)
One of the two parallel sides of a trapezoid.
If the top of the trapezoid is 6 ft, then b₂ = 6 ft; both bases are parallel to each other
Base 2 (b2)
The other parallel side of a trapezoid.
A dashed vertical line from the top base straight down to the bottom base at a 90° angle — NOT the slanted side
Height
The straight-up distance between the two parallel sides.
A trapezoid with b₁ = 10, b₂ = 6, h = 4 has area = ½(10 + 6) × 4 = 32 sq units
Area
How much space is inside a flat shape.
Key Ideas & Notes
- Your architecture firm is designing a trapezoidal window for a modern building.
- The glass supplier charges by the square foot, so the team must calculate the exact area.
- The window has a top edge of 4 feet, a bottom edge of 8 feet, and a height of 5 feet.
- Plot the vertices of a trapezoid with bases of 8 and 4, and height of 5. Place points at (0, 0), (8, 0), (6, 5), and (2, 5).
Think About It
- What shape is the window?
- How many parallel sides does it have?
- What measurements are given?
My Notes
Guided Examples
Example 1
What is the area of a trapezoid with bases 6 cm and 10 cm, and height 4 cm?
Solution: A = ½ × (b₁ + b₂) × h = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 sq cm.
Answer: A. 32 sq cm
Example 2
A trapezoid has an area of 45 sq ft, bases of 7 ft and 11 ft. What is the height?
Solution: A = ½ × (b₁ + b₂) × h → 45 = ½ × 18 × h → 45 = 9h → h = 5 ft.
Answer: A. 5 ft
Example 3
What is the first step when finding the area of a trapezoid?
Solution: The formula is A = ½ × (b₁ + b₂) × h. The first step is to add the two parallel bases.
Answer: A. Add the two bases together
Write About the Math The Writing Revolution
I can explain my steps using the words trapezoid, base, height, and area.
1. Kernel Sentence subject + verb
Model: Trapezoid is a four-sided shape with just one pair of parallel sides.Trapecio es una figura de cuatro lados con solo un par de lados paralelos.
Write a kernel sentence about trapezoid. Use a subject and a verb.Escribe una oración base sobre trapecio. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Trapezoid matters in mathTrapecio importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Trapezoid matters in math because ___.Trapecio importa en matemáticas porque ___.
Trapezoid matters in math, but ___.Trapecio importa en matemáticas, pero ___.
Trapezoid matters in math, so ___.Trapecio importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about trapezoid.Di un hecho verdadero sobre trapezoid.
Trapezoid ___.
Ask a question about trapezoid.Haz una pregunta sobre trapezoid.
How does ___ ?¿Cómo ___ ?
Show excitement about trapezoid.Muestra entusiasmo sobre trapezoid.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with trapezoid.Dile a un compañero qué hacer con trapezoid.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I added the two bases because ___.Sumé las dos bases porque ___.
The area is ___.El área es ___.
I see trapezoids in ___.Veo trapecios en ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is the first step when finding the area of a trapezoid?
- Add the two bases together
- Multiply the two bases
- Subtract the shorter base from the longer base
- Divide the height by 2
2. A trapezoid has bases of 5 in and 9 in, and a height of 6 in. What is its area?
- 42 sq in
- 84 sq in
- 27 sq in
- 30 sq in
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A trapezoid and a parallelogram both have a height of 8 ft. The trapezoid has bases of 5 ft and 11 ft. The parallelogram has a base of 8 ft. Which shape has the greater area? Explain your reasoning using the formulas.
Sentence starter: The trapezoid's area is ___ because ½ × (___ + ___) × ___ = ___. The parallelogram's area is ___ because ___ × ___ = ___. The ___ has a greater area by ___ sq ft.
Reflect — Exit Ticket
A trapezoid has bases of 9 inches and 5 inches, and a height of 6 inches. What is its area?
- 42 sq in
- 84 sq in
- 27 sq in
- 42 in
Answer Key & Teacher Guide
- Try It 1: A. Add the two bases together — The formula is A = ½ × (b₁ + b₂) × h. The first step is to add the two parallel bases.
- Try It 2: A. 42 sq in — A = ½ × (5 + 9) × 6 = ½ × 14 × 6 = ½ × 84 = 42 sq in.
- Exit Ticket: A. 42 sq in — A = 1/2 x (b1 + b2) x h = 1/2 x (9 + 5) x 6 = 1/2 x 14 x 6 = 42 square inches.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Trapezoid is a four-sided shape with just one pair of parallel sides.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).