*Contributor: Erika Wargo. Lesson ID: 12584*

Triangles show up in all kinds of places, not just geometry lessons. They're on maps, blueprints, cheese wedges, pool tables; etc. So it's important (and easy) to learn the angle on figuring out area!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Lion, Beaver

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

The Bermuda Triangle covers about 500,000 square miles (area) of ocean off the coast of Florida. How do you find the area of a triangle? What information is needed?

*Area* is the number of square units needed to cover a surface.

The area of shapes such as rectangles and squares is found by multiplying the length by the width. To find the area of a triangle, you have to use a different formula.

- What do you notice about the rectangle and triangle below?
- What do you think the formula for a triangle is, based on the images and what you already know about finding the area of a rectangle?

Think about each question and then write a response in your math journal or discuss with a parent or teacher:

Next, you will watch a video that explains the formula for finding the area of a triangle.

Answer the questions below in your math journal based on the information in the video:

- The formula for finding the area of a triangle is: ________________.
- How can you use a square or rectangle to find the area of a triangle?
- Draw a triangle and label the base and height.
- Review: What classifies a triangle as an acute, an obtuse, or a right triangle?

Discuss the questions above with a parent or teacher after watching the video clip, *Math Antics - Area *(NOTE: The relevant clip begins at 4:47 and ends at 10:10.):

Now, you will practice finding the area of a triangle by completing the following steps:

- Go to Area of a Triangle (Scholastic StudyJams!) and click on the STEP BY STEP button to watch how to calculate the area of a triangle. Click on the NEXT and SHOW ME buttons to progress through the steps.
- Click on WATCH OUT! to learn about finding the height and base of a triangle. These two steps are very important when finding the area of a triangle.
- Click on TRY IT! to practice finding the area of a triangle. Show the steps of your work in your math journal.

The base of the triangle is a side of the triangle, but it doesn’t always have to be the bottom side. You can think of the base as the bottom portion of the triangle similar to how your feet are the base of your body, as long as the height meets at the base to form a right angle.

The height of the triangle doesn’t have to be a side of the actual triangle, but it will meet with the base of your triangle to form a right angle. The height can be thought of as the tallest part of the triangle, either a side of the triangle or an imaginary line drawn into the triangle. If you went to the doctor and they measured how tall you were, you wouldn’t stand diagonally. You would stand up straight and tall.

The formula for finding the area of a triangle is Area = ½(base)(height). The units are squared since you are solving for area; for example, in^{2} or cm^{2}. The unit would be read as “square inches” or “square centimeters.”

You can use this formula in a few different ways:

- Multiply the base and height first, then multiply by one-half (½).
- Multiply the base and height first, then divide by 2.
- Multiply the base by ½ and then take that number and multiply it by the height.

Remember, multiplying by ½ and dividing by 2 will give you the same number!

For example, ½ x 10 = 5 and 10 ÷ 2 = 5.

In your math journal, write a response to the following:

- In your own words, what is area?
- How is finding the area of a triangle different from the area of a rectangle?
- Explain why the formula for finding the area of a triangle includes ½ or dividing by 2.

In the *Got It?* section, you will practice finding the area of triangles as you play interactive games and complete interactive practice.

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