There is a six-sided object.When a hexagon is regular it has six side lengths.Apothem is a line segment from the center of a circle to the middle of the circle.When calculating the area of a hexagon, you need to know the length of the apothem.If you know the side length of the hexagon, you can calculate the length.
Step 1: Six equilateral triangles are divided into the hexagon.
Draw a line from one point to another.
Step 2: To label the length of a triangle, you have to choose one.
This is the same length as the hexagon.You could have a hexagon with a side length of 8 cm.The equilateral triangle's base is 8 cm.
Step 3: Make two right triangles.
Draw a line from the top of the equilateral triangle to its base.The base of the triangle will be cut in half by this line.The base of one of the right triangles should be labeled.When you divide the equilateral triangle into two right triangles, each right triangle now has a base of 4 cm.
Step 4: The Pythagorean Theorem requires a formula.
There is a formula where the length of the hypotenuse is equal to the side opposite the right angle.For example, if a right triangle had a hypotenuse of 2 inches, one leg of 1 inch, and another leg in the same size.
Step 5: The length of the right triangle should be plugged into the formula.
Substitute for displaystyle b.The formula will look like this if the base is 4 cm.
Step 6: The length of the hypotenuse should be plugged into the formula.
You know how long the hypotenuse is because you know the side length.The side length of a regular hexagon is the same as the radius.The central point of a polygon is connected by a line called the radius.The side length of the hexagon is equal to the hypotenuse of your right triangle.If the side length of the hexagon is 8 cm, then the right triangle's hypotenuse is as well.The formula will look like this.
Step 7: The formula has known values.
Squared a number means to multiply it by itself.Your formula will look like this if you square the known values.
Step 8: The unknown variable needs to be isolated.
If you want to do this, subtract the squared value from both sides of the equation.For example, a display style is a2+16-16.
Step 9: It's possible to solve for a display style.
Find the square root of each side of the equation.This will give you the length of the missing side, which is the same length as the apothem.You can use a calculator to calculate 48=6.93displaystyle.The missing length of the right triangle is 6.93 cm.
Step 10: The formula should be used to find the apoth of a regular polygon.
The side is equal to the side of the formula.
Step 11: The side length needs to be plugged into the formula.
Substitute for the variable displaystyle s.For a hexagonal with a side length of 8 cm, the formula will look like this.
Step 12: Put the number of sides into the formula.
There is a hexagonal structure with 6 sides.Substitute for the variable ndisplaystyle.The display style is 82tan.
Step 13: The calculation can be completed in parentheses.
The degrees you use to calculate the tangent are found here.The formula now looks like this: 82tan(30)displaystylefrac 82tan(29).
Step 14: Find the point.
You can use a calculator to do this.The formula will now look like this: 82(.577)displaystyle frac8"
Step 15: Divide the side length by the number 2.
This will show you the length of your hexagon.For example_apothem=82(.577)displaystyle textapom