Unit 5 · Standard 6.G.1
Area of Parallelograms
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Think of a leaning door — the top and bottom are parallel, and the two sides are parallel, like a slanted rectangle
Parallelogram
A four-sided shape with two pairs of parallel sides.
If the bottom of a parallelogram is 10 cm, then b = 10 cm in the formula A = b × h
Base
A side of the shape you use to find the area.
A dashed vertical line from the top side straight down to the base, forming a 90° angle — NOT the slanted side
Height
The straight-up distance from the base to the top.
A 3 cm × 4 cm rectangle covers 12 square centimeters — imagine 12 tiny 1×1 squares inside it
Area
How much space is inside a flat shape.
An L-shaped room = a 10×8 rectangle joined to a 4×5 rectangle; total area = 80 + 20 = 100 sq ft
Composite figure
A shape made by putting two or more simple shapes together.
A = b × h means Area equals base times height; for a parallelogram with b = 6 and h = 4, A = 24
Formula
A math rule written with symbols.
Key Ideas & Notes
- Your architecture firm is designing a parallelogram-shaped patio for a client's backyard.
- The client needs to know how many square feet of pavers to order.
- The patio has a base of 14 feet and a height of 9 feet.
- Plot the vertices of a parallelogram with base 14 and height 9. Place points at (0, 0), (14, 0), (16, 9), and (2, 9) to visualize the patio.
Think About It
- What shape is the patio?
- What measurements are given?
- How is a parallelogram different from a rectangle?
My Notes
Guided Examples
Example 1
What is the area of a parallelogram with base 10 cm and height 7 cm?
Solution: A = b × h = 10 × 7 = 70 square centimeters.
Answer: A. 70 sq cm
Example 2
A parallelogram has an area of 54 sq ft and a base of 9 ft. What is the height?
Solution: A = b × h → 54 = 9 × h → h = 54 ÷ 9 = 6 ft.
Answer: A. 6 ft
Example 3
What is the area of a parallelogram with base 9 cm and height 5 cm?
Solution: A = b × h = 9 × 5 = 45 square centimeters.
Answer: A. 45 sq cm
Write About the Math The Writing Revolution
I can explain how I found the area using the words base, height, area, and formula.
1. Kernel Sentence subject + verb
Model: Parallelogram is a four-sided shape with two pairs of parallel sides.Paralelogramo es una figura de cuatro lados con dos pares de lados paralelos.
Write a kernel sentence about parallelogram. Use a subject and a verb.Escribe una oración base sobre paralelogramo. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Parallelogram matters in mathParalelogramo importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Parallelogram matters in math because ___.Paralelogramo importa en matemáticas porque ___.
Parallelogram matters in math, but ___.Paralelogramo importa en matemáticas, pero ___.
Parallelogram matters in math, so ___.Paralelogramo importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about parallelogram.Di un hecho verdadero sobre parallelogram.
Parallelogram ___.
Ask a question about parallelogram.Haz una pregunta sobre parallelogram.
How does ___ ?¿Cómo ___ ?
Show excitement about parallelogram.Muestra entusiasmo sobre parallelogram.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with parallelogram.Dile a un compañero qué hacer con parallelogram.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
Area equals base times ___.El área es la base por ___.
It is like a rectangle because ___.Es como un rectángulo porque ___.
I see this shape in ___.Veo esta forma en ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is the area of a parallelogram with base 9 cm and height 5 cm?
- 45 sq cm
- 14 sq cm
- 22.5 sq cm
- 90 sq cm
2. Which measurement is the height of a parallelogram?
- The perpendicular distance between the base and the opposite side
- The length of the slanted side
- The perimeter divided by 4
- The longest side
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A parallelogram has a base of 12 cm. If you double the height, the area doubles too. Explain why this happens using the formula, and give a specific example with numbers.
Sentence starter: When the height doubles from ___ to ___, the area changes from ___ to ___ because in the formula A = b × h, the base stays at ___ and ___.
Reflect — Exit Ticket
A parallelogram has a base of 13 inches and a height of 5 inches. What is its area?
- 65 sq in
- 36 sq in
- 18 sq in
- 65 in
Answer Key & Teacher Guide
- Try It 1: A. 45 sq cm — A = b × h = 9 × 5 = 45 square centimeters.
- Try It 2: A. The perpendicular distance between the base and the opposite side — The height is always the perpendicular (straight up-and-down) distance between the base and the opposite side, not the slanted side.
- Exit Ticket: A. 65 sq in — A = b x h = 13 x 5 = 65 square inches.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Parallelogram is a four-sided shape with two pairs 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).