Download 1. To introduce the topic show students a clip from

1. To introduce the topic show students a clip from Sonny With a Chance (season 1,
episode 5). In it Sonny has been doing bad at math and she has a big geometry test coming up. In
one scene Zora tries to explain geometry with a model. She says that a hexagon is made up of six
triangles. The model has six triangles, each a different color, that are stuck together to form a
hexagon. She pulls one triangle off and explains that if you find the area of one triangle you can
find the area of the hexagon. The clip can be found here:
https://www.youtube.com/watch?v=dXHdXpd3Te4.
2. Show students this printed model that is similar to the model used in the television
show. You can print just one copy to pass around or have several for students to play with.
3. Have students prove that this is a regular hexagon.
In a regular hexagon the sum of the interior angles will be (6-2)180 = 720 degrees. Since each
angle is equivalent, the measure of each interior angle will be 720/6 = 120 degrees. Each triangle
is equilateral, which means all angles in the triangles are 60 degrees. Since each angle in the
hexagon is made up of two angles of a triangle, it is 120 degrees.
4. Ask students to find the area of the hexagon.
As Zora started to explain, to get the area of the hexagon it is only necessary to know the area of
one of these equilateral triangles. Each triangle is the same since the hexagon is regular and we
know all sides have the same length. That means the area of the hexagon will be six times the
area of one of the triangles. For example, if each side has length 5 cm then we can take one of
the equilateral triangles and we know each side of it has a length of 5 cm. To find the area of the
triangle we can draw a perpendicular to form two right triangles. The hypotenuse is still 5 cm
and the base will be 2.5 cm because it was bisected. Thus, the height can be found by solving h2
+ 2.52 = 52. The height is found to be
1 5 5√3
is 2 (2 (2)
2
)=
25√3
4
5√3
2
cm. This means that the area of the equilateral triangle
cm2. Thus, the area of the hexagon is
75√3
2
cm2.
5. What other shapes can be made out of equilateral triangles? Try to make a triangle. What
would the area be?
Each angle is 60 degrees in the smaller equilateral triangles so we know the
sum of the angles in the larger triangle is 180 degrees. It formed a larger
equilateral triangle. The area is 4(the area of the triangle).
Try to make a rhombus. What would the area be?
We know opposite angles are equal (two are 60 and the other two are 120) and
sides are all equal length since they are all sides of the equilateral triangle. The
area is 2(the area of the triangle).
What other shapes can you make out of equilateral triangles? What would the area be?
One example is this start that you can make by starting with a hexagon then putting an
equilateral triangle on top of each side. The area is 12(the area of the triangle).