2.10 Perimeter and Area
Triangles and Parallelograms
The Importance of Units –Students will give answers that do not include the proper units, unless it is required
by the instructor. When stating an area, square units should be included, and when referring to a length, linear
units should be used. Using proper units helps reinforce the basic concepts. With these first simple area problems
including the units seems like a small detail, but as the students move to more complex situations combining length,
area, and volume, units can be a helpful guide. In physics and chemistry dimensional analysis is an important tool.
The Power of Labeling –When doing an exercise where a figure needs to be broken into polynomials with known
area formulas, it is important for the student to draw on and label the figure well. Each polygon, so far only
parallelograms and triangles, should have their base and height labeled and the individual area should be in the
center of each. By solving these exercises in a neat, orderly way student will avoid errors like using the wrong
values in the formulas, overlapping polygons, or leaving out some of the total area.
Subtracting Areas –Another way of finding the area of a figure that is not a standard polygon is to calculate a
larger known area and then subtracting off the areas of polygons that are not included in the target area. This can
often result in fewer calculations than adding areas. Different minds work in different ways, and this method might
appeal to some students. It is nice to give them as many options as possible so they feel they have the freedom to be
creative.
The Height Must Be Perpendicular to the Base –Students will frequently take the numbers from a polygon and
plug them into the area formula without really thinking about what the numbers represent. In geometry there will
frequently be more steps. The students will have to use what they have learned to find the correct base and height
and then use those numbers in an area formula. Remind students that they already know how to use a formula; many
exercises in this class will require more conceptual work.
Write Out the Formula –When using an area formula, it is a good idea to have the students first write out the
formula they are using, substitute numbers in the next step, and then solve the resulting equation. Writing the
formula helps them memorize it and also reduces error when substituting and solving. It is especially important
when the area is given and the student is solving for a length measurement in the polygon. Students will be able to
do these calculations in their heads for parallelograms, and maybe triangles as well, but it is important to start good
habits for the more complex polygons to come.
Trapezoids, Rhombi, and Kites
It’s Arts and Crafts Time –Student have trouble remembering how to derive the area formulas. At this level
it is required that they understand the nature of the formulas and why the formulas work so they can modify and
apply them in less straightforward situations. An activity where student follow the explanation by illustrating it with
shapes that they cut out and manipulate is much more powerful then just listening and taking notes. It will engage
the students, keep their attention, and make them remember the lesson longer.
Trapezoid
a. Have student use the parallel lines on binder paper to draw a trapezoid. They should draw in the height and2.10. Perimeter and Area