Slide 1:Connections In Areas: Rectangles & Triangles By Renee Hill Stephanie Lessman Linda Stein TTTC Math & Technology Summer 2001


Today’s Goal: Determine the formula for the area of a triangle. :Today’s Goal: Determine the formula for the area of a triangle. California Standard – Grade Five Measurement and Geometry 1.1 (partial) Derive and use the formula for the area of a triangle by comparing it with the formula for the area of a rectangle.


: What are the properties of a rectangle?


Properties of a Rectangle :Properties of a Rectangle There are four right angles.


Properties of a Rectangle :Properties of a Rectangle There are two sets of parallel sides opposite one another.


Area of Rectangle :Area of Rectangle Identify the area of the rectangle. This is the area of the rectangle.


Calculating the Area :Calculating the Area Determine the area of this rectangle if the length is 8 units and the width is 3 units. 3 units 8 units The area of this rectangle is 24 square units.


Writing the Equation and the Formula :Writing the Equation and the Formula 3 units 8 units The area of this rectangle is 24 square units. width length times equals area 8 units x 3 units = 24 square units Equation: Formula:


The Rectangle-Triangle Connection :The Rectangle-Triangle Connection How can you divide this rectangle into two equal triangles?


The Solution :The Solution There are two solutions.


The Triangle-Rectangle Connection :The Triangle-Rectangle Connection What is the area of the triangle A and triangle B combined? Triangle A Triangle B


The Solution :The Solution The combination of Triangle A and Triangle B has an area equal to the rectangle. Triangle A Triangle B


The Triangle Disconnection :The Triangle Disconnection Is it possible to calculate the area of one of these triangles? Yes!


Half-Size It :Half-Size It 3 units 8 units Note that Triangle A is half of the area of the rectangle.


Where We Started :Where We Started 3 units 8 units Remember that the area of the rectangle was 24 square units?


Writing the Equation :Writing the Equation 3 units 8 units The rectangle area equation was: The triangle area equation is half the rectangle: ( ) 12


Equation vs. Formula :Equation vs. Formula The triangle area equation is: ( ) 12 The triangle area formula uses the labels in place of the numbers.


The Equation – Formula Connection :The Equation – Formula Connection 8 units x 3 units = square units The triangle area equation is: ( ) 12 length x width = area The triangle area formula is: ( )


Use What You Know :Use What You Know Use your knowledge of rectangles and triangles to determine the area of more complex figures. l x w (l x w)


What’s Next? :What’s Next? In our next lessons, we will explore these questions: and . . . What about circles? What is the formula for the area of a parallelogram? Does this work for all types of triangles?