Exploring the Area of a Triangle


I can: 

I can identify the formula for area of a triangle.

I can identify the base and height of a triangle.

I can apply the formula for area of a triangle.

I can find the area of irregular polygons.


Tech Skills: 

Drag and Drop

Selecting Objects

Graphing

Typing (Calculator)





Procedure: 
Activity 1: Exploring Area of a Triangle

Draw a rectangle on the board and ask students how they would find the area.

Once students discuss, write the area of a rectangle on the board and tell the students they will be using their knowledge of area of a rectangle to discover what the area of a triangle is.

Have students go to the Geogebra website and follow the instructions below.

Click the show/hide triangle box to hide the triangle. Move the sliders to a desired number and calculate the area of the rectangle (see area listed on the left).

Click the show/hide boxes to show the triangle and hide the rectangle. Notice the area of the triangle listed as well as the length of the base and height.
 Use the sliders to change the lengths and record all information listed below:
Length of Base
Height
Area of Rectangle
Area of Triangle
 Have students answer the following questions and then compare with a partner.
What do you notice about the relationship of the areas of the rectangle and triangle?
Write separate formulas for the area of a rectangle and area of a triangle:
What would the area of 2 triangles be? How does it relate to the rectangle?
Activity 2

Now that students know the area of a rectangle and area of a triangle, have them work in partners to find the area of irregular polygons.

Students will go to the Vertical Learning website.

After the students have had time to solve a couple of problems. Choose a few students to explain how they were solving the problems.

Ask the students if there is another way to solve the problems. See if any of the students discovered they could also find the area of the larger rectangle and then subtract missing polygon areas.

Do the the following activity as either whole class or individually on geogebra.org.

A room in my house is 120 square feet. Use a combination of rectangles and right triangles and rectangles to draw three possible shapes that my room could be.
Practice Activity
Area of Triangle Game/Quiz 

Standards: 
CCSS.MATH.CONTENT.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 

