Area of Triangles and Trapezoids

This lesson is based from the textbook Holt Middle School Math:  Course 2.
Bennet, J.M., Chard, D.J., Jackson, A., Milgram, J., Scheer, J.K., Waits, B.K.  (2004).  Holt middle school math:  Course 2.  Orlando:  A Harcourt Education Company.

Lesson Title:  Finding Areas
Grade Level:  7th grade                                    
Course Title:  Compacted Math
Time Allotted:  1 class period                     
Number of Students:
  24-34 students                             
Extra Information About Students: 
Day 4

Goals and Objectives:

According to the NCTM Principles and Standards of Mathematics, the following standards are met in this lesson:
1.   To understand measurable attributes of objects and the units, systems, and processes of measurement.

2.   To apply appropriate techniques, tools, and formulas to determine measurements.

According to the NCSCOS, the following standards are met in this lesson:

1.   Competency Goal 2:  The learner will demonstrate an understanding and use of the properties and relationships in geometry, and standard units of metric and customary measurement.


Materials Needed and/or Use of Space:

Math Fact of the Day:

The line connecting the midpoints of the two nonparallel segments of a trapezoid is called the midsegment.

Problem of the Day:

An isosceles trapezoid has bases 7 in. and 4 in. and heigh 1.5 in.  Find its area by using only the formula for the area of the parallelogram.  Draw a picture, too.

Motivational Activity:

The students will learn about how to find the area of triangles and trapezoids today. 

Before teaching the lesson, you should review the parts of the triangle, particularly the altitude and base of the triangle.  Other things to review include the following:
After reviewing this, explain to the students some information about the Bermuda Triangle. 

Lesson Procedure:

Yesterday we learned how to find the area of parallelograms.  Today we are going to discuss how to find the areas of triangles and trapezoids.  When looking at a parallelogram, we notice that the diagonal of a parallelogram divides the parallelogram into two congruent triangles.  (Draw on the board if necessary for students to see).  Thus, the area of each triangle is half the area of the parallelogram.


The base of a triangle can be any side.  The height of a triangle is the perpendicular distance from the base to the opposite side.

Here is a chart similar to those we looked at yesterday to help you understand how to find the area of a triangle, along with a picture to help you learn.


The area A of a
triangle is half
the product of its
base b and its height h.

A=1/2 bh


Now that we know what area is and how to find the area of a triangle, let's do an example together!

Example 1:  Find the area of the triangle.


We use the formula and substitute for l and w.
A=14 square units

Thus, the area of the rectangle is 14 square units.
A parallelogram can be divided into two congruent triapezoids.  The area of each trapezoid is one-half the area of the parallelogram.


The two parallel sides of a trapezoid are its bases.  If we call the longer side b1 and the shorter side b2, then the base of the parallelogram is b1+b2.


The area A of a trapezoid
is half its height
multiplied by the sum
of the lengths of its
two bases.



Example 2:  Find the area of the trapezoid.


A=1/2(5 cm)(2.5 cm + 6 cm)
A=(2.5 cm)(8.5 cm)
A= 21.25 square centimeters.

Thus, the area of our trapezoid is 21.25 square centimeters.

Now that we know how to find the area of a triangle and the area of a trapezoid, let's do an activity utilizing the new concepts that we have just learned.



If an extension activity is needed, the students can think and write responses to the following questions:


Review with the students the various formulas that they have learned thus far - circumference, area of a parallelogram, triangle, and trapezoid.  Have students come up to the board and write the formulas and have other students come up to the board and draw the specific diagram that corresponds with the specific formula.

As you can see, we have learned how to find the area of triangles and trapezoids.  As we saw in one of our examples, we utilize this concept in the real world sometimes.  This is an important component that will be of use in your future with whatever you do.  Tomorrow we will discuss finding the area of circles and see how that is different from what we have been discussing the past two days - the areas of parallelograms, triangles, and trapezoids. 


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