Area of Triangles and
This lesson is based from the textbook Holt Middle School Math: Course 2.
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
Lesson Title: Finding Areas
Grade Level: 7th grade
Course Title: Compacted Math
Time Allotted: 1
Number of Students: 24-34 students
Information About Students: None
According to the NCTM Principles and Standards of
following standards are met in this lesson:
1. To understand measurable attributes of objects and
the units, systems, and processes of measurement.
- Understand both
metric and customary systems of measurement.
relationships among units and convert from one unit to another within
the same system.
select, and use units of appropriate size and type to measure angles,
perimeter, area, surface area, and volume.
To apply appropriate techniques, tools, and formulas to determine
and use formulas to determine the circumference of circles and the area
of triangles, parallelograms, trapezoids, and circles and develop
strategies to find the area of more-complex shapes.
According to the NCSCOS, the following
standards are met in this lesson:
2: The learner will demonstrate an understanding and use of the
properties and relationships in geometry, and standard units of metric
and customary measurement.
- For the
students to understand how to find the areas of triangles and
- For the
students to apply this information to their everyday encounters.
and/or Use of Space:
- Graph Paper
Math Fact of the
line connecting the midpoints of the two nonparallel segments of a
trapezoid is called the midsegment.
- Share this
with the students at the beginning of class. It is similar to
when an English teacher shares a quote at the beginning of language
Problem of the Day:
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.
- Give this
to the students at the beginning of class and have them turn in their
answers with their unit portfolio at the end of the unit. The
answer for this problem is: (5.5)(1.5)=8.25
problem is an introduction into the day's lesson.
students should be able to solve this problem after today's lesson.
will learn about how to find the area of triangles and trapezoids
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:
this, explain to the students some information about the Bermuda
- Draw an
acute triangle on the board.
- Define the
base of the triangle as any side of the triangle and label it.
- Draw the
altitude that corresponds to the base.
- Be sure to
explain that the altitude is the perpendicular segment from a vetex of
the triangle to the opposite base.
- The height
of the triangle is the length of the altitude.
Bermuda Triangle is a triangular region between Bermuda, Florida, and
Puerto Rico. The Bermuda Triangle is an interesting
phenomenon. More information about this phenomena can be found at
website may be an interesting resource to explore if there is enough
time AND if the students all have access to computers. A webquest
could possibly be made in correspondence with this website. This
would provide the students with a technology component during class.
- In order
to find the area of this region, you could use the formula that we will
learn today to find the area of a triangle! This formula is
closely related to the formula used to find the area of the
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
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.
AREA OF A TRIANGLE
The area A of a
triangle is half
the product of its
base b and its height h.
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.
can be divided into two congruent triapezoids. The area of each
trapezoid is one-half the area of the parallelogram.
- Note: Our units are in square units. Make sure to
point this out to students and to explain that because we do not have a
specific unit of measurement to use, that we assume the measurement to
be in units.
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.
OF A TRAPEZOID
area A of a trapezoid
is half its height
multiplied by the sum
of the lengths of its
Remind the students the difference between b1 and b2 - I think that it
will become more clear when doing an example together.
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
- Have the
students get into small groups - probably 3 or 4 depending upon how
many students are in the class. Today, separate the groups based
on the letters of their first names; put the first 3 people with
A-names together, the next 3 people who have B-names, and continue on
until there are groups with 3-4 students in each group.
- Have the
students draw a triangle (with the use of a ruler) whose lengths have
whole number measures. Make sure to note that the triangle should
fit on the piece of graph paper that was given to them.
- Now have
the students cut out the triangle and use the formula to show that any
of the three sides can serve as the base of the triangle.
- In order
to find the height, students can draw a rectangle around the cutout
triangle on another sheet of graph paper to find the height of the
triangle for each base.
activity is good for those who are visual learners and kinesthetic
teacher should provide scaffolding to the students so that they
understand the big picture and see what is going on.
questions to ask are:
- Why do
we need to make sure that we are using whole numbers for the lengths of
- What is
another way that we can find the height of our triangle?
- How is
this particular activity helpful to your learning process?
an extension activity is needed, the students can think and write
responses to the following questions:
- Tell how
to use the sides of a right triangle to find its area.
how to find the area of a trapezoid.
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.
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.
will complete the problem of the day. Their completion
of this problem will show the teacher whether or not they understand
what they have learned in class that day. This activity also
teaches the students more
about mathematical communication.
students will also have a worksheet to complete. If the worksheet
is not completed in class, it is to be finished as homework. This
worksheet will count as a homework grade.
students are expected to participate in the activity, too. This
will be part of their classwork grade and their behavior/conduct grade.
- What would you
- What would you
do the same?
- Was this a good
lesson - why or why not?