and compare it to the previous section. Mix-up exercises so students will see the similarities and learn each more
thoroughly.
Don’t Forget the Units –Remind students that when they calculate an area the units are squared. When an answer
contains the pi symbol, students are more likely to leave off the units. In the answer 7πcm^2 , theπis part of the
number and the cm^2 are units of area.
Draw a Picture –When applying geometry to the world around us, it is helpful to draw, label, and work with
a picture. Visually organize information is a powerful tool. Remind students to take the time for this step when
calculating the areas of the irregular shapes that surround us.
Additional Exercises:
- What is the area between two concentric circles with radii 5 cm and 12 cm?
(Hint: Don’t subtract the radii.)
Answer: 144π− 25 π= 119 πcm^2
- The area of a sector of a circle with radius 6 m, is 12πcm^2. What is the measure of the central angle that defines
the sector?
Answer:
12 π=x
360
∗π∗ 62 The central angle measures 120 degrees.
x= 120- A square with side length 5
√
2 cm is inscribed in a circle. What is the area of the region between the square and
the circle?
Answer:π∗ 52 −( 5
√
2 )^2 = 25 π− 50 ≈ 28 .5 cm^2Regular Polygons
The Regular Hypothesis –Make it clear to students that these formulas only work for regular polygons, that is,
polygons will all congruent sides and angles. The regular restriction is part of the hypothesis. Many times the
hypotheses of important theorems in mathematics are quite restrictive, but that does not necessarily limit the value
of the theorem. If a polygon is approximately regular, then the formula can be used to get an approximate area. Also,
the method of breaking the polygon into triangles can be applied to non-regular polygons, but each triangle may be
different and therefore each area computed separately. It is important to understand how the theorem or formula
was derived so it can be adapted to other situations. Knowing this will motivate students to work to understand the
formulas.
Numerous Variables and Relationships –Polygons come with an entire new set of variable. Students need to
learn what these knew variable represent, how they are related to the triangles that makeup the polygon, and how
they are related to each other. This will take some time and practice. If students do not have time to memorize
what the variables represent, they will not understand how they are being put together in the various formulas. Find
convenient breaking points and give students time, examples, or activities to help them become familiar with the
material. If it all comes too fast, student will get lost and frustrated.
What isn? -Students will frequently be given the value ofn, but will not realize it because it is not given in the
form they are expecting. An exercise may state, “Each side of a regular hexagon is nine inches long.” The students
will see the nine and assign it to the variables, but not notice that they are also being given the value ofn; a hexagon
has six sides.
Chapter 2. Geometry TE - Common Errors