Table of Contents
- 1 How do you find the area of a hexagon with an apothem?
- 2 What is the area of a hexagon with an apothem of 4 square root 3?
- 3 What is the apothem of a hexagon?
- 4 What is the Apothem of a hexagon?
- 5 How do I find the length of the apothem?
- 6 How do you calculate the apothem of a hexagon?
- 7 How does the apothem divide the equilateral triangles?
How do you find the area of a hexagon with an apothem?
Calculating from a Regular Hexagon with a Given Apothem. Write down the formula for finding the area of a hexagon with a given apothem. The formula is simply Area = 1/2 x perimeter x apothem.
What is the area of a regular hexagon with an apothem of 3 ft?
The area of the hexagon is 23.383 ft2 .
What is the area of a hexagon with an apothem of 4 square root 3?
The area of a regular hexagon is 6 areas of equilateral triangles with a side equal to a side of a hexagon. Each such triangle has base a=4√3 and altitude (apothem of a hexagon) h=a⋅√32=6 .
How do you find the side length of a hexagon with the apothem?
If you only know the apothem, you can still find the length of a side by plugging the apothem into the formula a = x√3 and then multiplying the outcome by 2. It is because the apothem depicts the x√3 sides of the 30-60-90 triangle that it forms.
What is the apothem of a hexagon?
A hexagon is a six-sided polygon. When a hexagon is regular it has six equal side lengths and an apothem. An apothem is a line segment from the center of a polygon to the middle point of any one side. You usually need to know the length of the apothem when calculating the area of a hexagon.
What is apothem of a hexagon?
What is the Apothem of a hexagon?
Is the apothem equal to the side?
The apothem is always perpendicular to the side on which it ends. A regular polygon has all its sides and angles equal.
How do I find the length of the apothem?
We can also use the area formula to find the apothem if we know both the area and perimeter of a polygon. This is because we can solve for a in the formula, A = (1/2)aP, by multiplying both sides by 2 and dividing by P to get 2A / P = a. Here, the apothem has a length of 4.817 units.
How do you calculate apothem?
How do you calculate the apothem of a hexagon?
To calculate the apothem of a hexagon, start by dividing the hexagon into 6 triangles. Then, divide one of the triangles in half to create 2 right triangles. Next, plug the length of one of the right triangle’s base and hypotenuse into the Pythagorean Theorem.
What is the area of the regular hexagon?
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle’s the base is a hexagon’s side and the apothem functions as height) or: Shexagon = 6 ⋅ S△ = 6 (base)(height) 2 = 3(2 √3)Apothem⋅ Apothem = (6 √3)(Apothem)2 => Shexagon = 6 ×62 √3 = 216 √3
How does the apothem divide the equilateral triangles?
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle’s radius, apothem and half of the hexagon’s side. Since the apothem forms a right angle with the hexagon’s side and since the hexagon’s side forms 60∘ with a circle’s radius with an endpoint in common with…
What is the formula for finding the apothem of a regular polygon?
Set up the formula for finding the apothem of a regular polygon. The formula is apothem=s2tan(180n){\\displaystyle {\ext{apothem}}={\\frac {s}{2\an({\\frac {180}{n}})}}}, where s{\\displaystyle s} equals the side length of the polygon and n{\\displaystyle n} equals the number of sides the polygon has.