Unit 5 · Standard 6.G.1
Area of Triangles
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
If the bottom of a triangle is 10 cm, then b = 10 cm in the formula A = ½ × b × h
Base
A side of the triangle you use to find the area.
A dashed vertical line from the top point straight down to the base at a 90° angle — like dropping a plumb line
Height
The straight-up distance from the base to the top corner.
A triangle with b = 8 and h = 6 has area = ½ × 8 × 6 = 24 sq units — exactly half the rectangle around it
Area
How much space is inside a flat shape.
The corner of a book or a door frame — the edges meet at exactly 90°, shown by a small square symbol
Perpendicular
Two lines that meet to make a square corner (90 degrees).
A house shape = a rectangle (the walls) + a triangle (the roof); total area = rectangle area + triangle area
Composite figure
A shape made by putting two or more simple shapes together.
A = ½ × b × h means Area equals one-half times base times height; for b = 12 and h = 8, A = 48
Formula
A math rule written with symbols.
Key Ideas & Notes
- Your architecture firm is designing a park with triangular garden beds.
- The client wants to know exactly how much soil to order, which means calculating the area of each triangular section.
- The first garden has a base of 12 feet and a height of 8 feet.
- Plot the vertices of a triangle with base 12 and height 8 to visualize the garden. Place points at (0, 0), (12, 0), and (6, 8).
Think About It
- What shape are the garden beds?
- What measurements do we need to find the area?
- How is the area of a triangle related to the area of a rectangle?
My Notes
Guided Examples
Example 1
What is the area of a triangle with base 10 cm and height 6 cm?
Solution: A = ½ × b × h = ½ × 10 × 6 = 30 square centimeters.
Answer: A. 30 sq cm
Example 2
A triangle has an area of 24 sq ft and a base of 8 ft. What is the height?
Solution: A = ½ × b × h → 24 = ½ × 8 × h → 24 = 4h → h = 6 ft.
Answer: A. 6 ft
Example 3
Why do we divide by 2 when finding the area of a triangle?
Solution: A triangle with base b and height h fits inside a rectangle with the same base and height. The triangle covers exactly half the rectangle, so A = ½ × b × h.
Answer: A. A triangle is exactly half of a rectangle with the same base and height
Write About the Math The Writing Revolution
I can explain my steps using the words base, height, area, and perpendicular.
1. Kernel Sentence subject + verb
Model: Area is how much space is inside a flat shape.Área es cuánto espacio hay dentro de una figura plana.
Write a kernel sentence about area. Use a subject and a verb.Escribe una oración base sobre área. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Area matters in mathÁrea importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Area matters in math because ___.Área importa en matemáticas porque ___.
Area matters in math, but ___.Área importa en matemáticas, pero ___.
Area matters in math, so ___.Área importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about area.Di un hecho verdadero sobre area.
Area ___.
Ask a question about area.Haz una pregunta sobre area.
How does ___ ?¿Cómo ___ ?
Show excitement about area.Muestra entusiasmo sobre area.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with area.Dile a un compañero qué hacer con area.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
A triangle is half of a ___.Un triángulo es la mitad de un ___.
So the area is ___.Entonces el área es ___.
I see triangles in ___.Veo triángulos en ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Why do we divide by 2 when finding the area of a triangle?
- A triangle is exactly half of a rectangle with the same base and height
- Triangles have 2 equal sides
- The base is always twice the height
- We always divide area formulas by 2
2. What is the area of a triangle with base 14 ft and height 6 ft?
- 42 sq ft
- 84 sq ft
- 20 sq ft
- 42 ft
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A rectangle is 12 ft by 8 ft. A diagonal line cuts it into two triangles. What is the area of each triangle? Explain how the triangle area formula relates to the rectangle area formula.
Sentence starter: The rectangle's area is ___ because ___. Each triangle's area is ___ because a diagonal splits a rectangle into ___ equal triangles, so A = ½ × ___ × ___ = ___.
Reflect — Exit Ticket
A triangle has a base of 11 inches and a height of 8 inches. What is its area?
- 44 sq in
- 88 sq in
- 19 sq in
- 44 in
Answer Key & Teacher Guide
- Try It 1: A. A triangle is exactly half of a rectangle with the same base and height — A triangle with base b and height h fits inside a rectangle with the same base and height. The triangle covers exactly half the rectangle, so A = ½ × b × h.
- Try It 2: A. 42 sq ft — A = ½ × 14 × 6 = ½ × 84 = 42 sq ft.
- Exit Ticket: A. 44 sq in — A = 1/2 × 11 × 8 = 1/2 × 88 = 44 square inches.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Area is how much space is inside a flat shape.
- 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).