Neft Teacher · Learn It

Unit 5 · Standard 6.GR.1

Determine the Area of Triangles

Lesson 5-2 · Learn It — how the math works

Why we're learning this

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.

✱ Math Workbench

Learn It

How do we find the area of a triangle?

A triangle has three sides. The base is one side, and the height is the straight-up (perpendicular) distance from the base to the top corner.

Picture itSee what the math looks like before you read about it

This is the firm's blueprint for a park. A rectangular plot is split by a diagonal path into two triangular garden beds that will be filled with soil.
Where you see this in real lifeThis is the firm's blueprint for a park. A rectangular plot is split by a diagonal path into two triangular garden beds that will be filled with soil.

Watch me solve itI do — read one step at a time

The problem looks like this
A triangle with a base of 12 feet and a perpendicular height of 8 feet. base = 12 feet height = 8 feet
  1. My triangular garden has a of 12 feet and a of 8 feet.
  2. I write the : A = ½ × × .
  3. I put in the numbers: A = ½ × 12 × 8.
  4. I multiply × first:12 × 8 = 96
  5. I take half: ½ × 96 = 48. So the is 48 square feet.

Watch out — mistakes students make here

  • 16 comes from adding 10 + 6. Area means multiply the base and height, then take half.
  • The number is right, but cm measures length. Area needs square units (sq cm).
  • 60 is base × height — the full rectangle. A triangle is half of that, so multiply by ½.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now a smaller triangle:base = 10 cm, height = 6 cm
  2. First, what is 10 × 6?10 × 6
    Check this step
    Yes, 60.
  3. Now take half: what is ½ × 60?
    Check this step
    Yes, 30.
  4. So the is 30 square centimeters.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember: multiply × , then take half.

Solve: What is the with 10 cm and 6 cm?

My answer

Stuck? Open one hint at a time.

Hint 1

You have a base of 10 cm and a height of 6 cm — a triangle needs only those two, plus one special step.

Hint 2

A triangle is half of a rectangle: use A = ½ × b × h. If you only multiply, your answer is twice too big.

Hint 3

Multiply 10 × 6, then take half of the product. Area units are square centimeters.

Check my answer
✅ Answer: 30 sq cm
A = ½ × b × h = ½ × 10 × 6 = 30 square centimeters.

Turn & TalkSay it out loud with a partner

The triangular garden bed has a of 12 feet and a of 8 feet. Which measurement is the height, and how is it different from the slanted side?

Try starting with:

  • The height is the ___ distance from the base to the top corner.La altura es la distancia ___ desde la base hasta la esquina de arriba.
  • It is different from the slanted side because ___.Es diferente del lado inclinado porque ___.
Use these wordsbaseheightperpendicularareaformula