Question

(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 side:
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:

Answer 1

Regular Hexagon area H = 24
`√(3)` sq. cm.

In a regular Hexagon, there are 6 equilateral triangles.

You create a 30-60-90 triangle when you cut an equilateral triangle in half.

The long side of the 30-60-90 triangle is called the "apothem"

Explanation:

You have one side of 4cm for the regular hexagon.

so then the shortest side of the 30-60-90 triangle is 2 cm.

the hypotenuse is therefore 4cm

and the long leg is equal to 2*root(3)

Height of one equilateral triangle = 2 root(3) cm.

Area of one of these equilateral triangles : A = (1/2)*2*root(3)*4cm

A = 4 root(3) sq. cm is area of one equilateral triangle.

Hexagon area : H = 6*A = 6*4*root(3) = 24 root(3)

H = 24
`√(3)` sq. cm.