Score for Question 3: ___ of 5 points)
3. Use the diagram of a REGULAR HEXAGON and follow these steps to solve for the area of a hexagon with sides equal to 4 cm. Leave radicals in your answers.

How many equilateral triangles are there?
If we cut an equilateral down the middle (green line) what special triangle do you create?
Sketch and label all side lengths of the 30-60-90 triangle by itself below.
What is the length of the short side of one 30-60-90 triangle?
What is the length of the hypotenuse of one 30-60-90 triangle?
Apply properties of 30-60-90 triangles to calculate the long leg: ¬¬¬¬
What is the vocabulary word for the long side of the 30-60-90 called in the polygon (green line)?
What is the height of the equilateral triangle?
Apply triangle area formula to calculate the area of one equilateral triangle:
Calculate the area of the complete hexagon by multiplying area of one equilateral triangle by # of triangles:

(a)6 Equilateral Triangles.

(b)30-60-90 triangle.

(c)See Attached Triangle in Figure 2

(d)Length of the short leg = 2cm.

(e)Length of the hypotenuse= 4cm.

(f)Length of the long leg=

(g)Apothem.

(h)Height of the Equilateral triangle=

(i)Area of One Equilateral triangle =

(j)Area of Hexagon =

Step-by-step explanation:

(a)From Figure 1, there are 6 Equilateral Triangles.

(b)If we cut an equilateral down the middle (green line), we create a 30-60-90 triangle.

(c)Triangle Attached in Figure 2.

(d)The length of the short leg of one of the 30-60-90 triangle is 2cm.

(e)The length of the hypotenuse of one of the 30-60-90 triangle is 4cm.

(f)Length of the long leg

We use Pythagoras Theorem to find the length of the long leg of the right triangle.

(g)The vocabulary word for the long side of the 30-60-90 called in the polygon (green line) is Apothem.

It is line segment from the center to the midpoint of one of the sides of a polygon.

(h)Height of the Equilateral Triangle=

(i)Area of One Equilateral triangle

Base =4 cm, Height =

Area=0.5X4X

=

(j)Area of Hexagon =Area of One Equilateral Triangle X 6