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The apothem is the radial distance from the middle of the side to the centre of the hexagon. A hexagon is six congruent equilateral triangles joined by adjacent sides. Equilateral triangles can be divided into two equal right angled triangles. The upright of the right angled triangle is effectively the apothem of the original hexagon. Pythagoras now kicks in.
The apothem (vertical) is A and half the side length (base) is B, the third (longest) side is C and is the same as the original side length. Pythagoras states A2 + B2 = C2. So by transposition, A = root (C2 - B2). As B = 1/2 C, the apothem A is given by:
A = root(C2 - (C/2)2) = root(C2 - C2/4) = root(3C2/4) = C x root(3) / 2
So the apothem of a hexagon is 1/2 x root(3) x the side length.
What else can I help you with?
How do you find the area of a hexagon without a side length?
To find the area of a Regular hexagon with side length (x) you need:1. The "radius" of the hexagon. (Just the length from the center to the outside edge.)2. The apothem. (which is only just half of the height of the base.)**If you don't have one or both of these you can't do it.**Steps:1. Make a triangle of the apothem (used as a) and the radius. (r)2. Use the Pythagorean Theorem to find 1 half of the side length.3. Multiply the actual side length by 6.4. Multiply that by a.5. The area is your answer.
What is the area of a regular hexagon with a side length of 4.5 m and an apothem length of 3.9 m?
Given the side length of a regular polygon you don't need the apothem and conversely. Using the side length, you get an area of 52.61 sq metres. Using the apothem, you get 52.69 sq metres. The difference between the two is because, if the side were exactly 4.5 m, then the apothem would be side*sqrt(3)/2. This is 3.897 m (to 3 dp) rather than 3.9. The difference leads to the answer for the area being 52.6 or 52.7 sq metres. However, the lengths are given to only 2 significant digits and to 2 sig digs, the area is 52 sq metres. This is a good example for people who insist on giving answers to spurious levels of accuracy.
What is the area of a regular hexagon with an apothem of 16.5 yards long and a side 19 yards long rounded to the nearest tenth?
16.5
How many diamonds make a hexagon?
It only takes to diamonds to form a hexagon, but three if it is a regular hexagon.
What does an irregular hexagon mean?
doesn't look like a hexagon, a shape with six sides only that are any lenght
How do you find the area of a hexagon without a side length?
To find the area of a Regular hexagon with side length (x) you need:1. The "radius" of the hexagon. (Just the length from the center to the outside edge.)2. The apothem. (which is only just half of the height of the base.)**If you don't have one or both of these you can't do it.**Steps:1. Make a triangle of the apothem (used as a) and the radius. (r)2. Use the Pythagorean Theorem to find 1 half of the side length.3. Multiply the actual side length by 6.4. Multiply that by a.5. The area is your answer.
What is the diameter of a hexagon with 10in sides?
there is no such thing as the diameter of a hexagon only circles can have diameters, now if u said the length horizontally or vertically that could be solved but since its a hexagon the length horizontally would be shorter than the length vertically.
What is the area of a regular hexagon with a side length of 4.5 m and an apothem length of 3.9 m?
Given the side length of a regular polygon you don't need the apothem and conversely. Using the side length, you get an area of 52.61 sq metres. Using the apothem, you get 52.69 sq metres. The difference between the two is because, if the side were exactly 4.5 m, then the apothem would be side*sqrt(3)/2. This is 3.897 m (to 3 dp) rather than 3.9. The difference leads to the answer for the area being 52.6 or 52.7 sq metres. However, the lengths are given to only 2 significant digits and to 2 sig digs, the area is 52 sq metres. This is a good example for people who insist on giving answers to spurious levels of accuracy.
Can a hexagon have unequal sides?
for sure, only a regular hexagon has equal sides. Hexagon just means 6 sides and they can be any length you want.
What is the area of a regular hexagon with 19 inch apothem and 12 inch sides?
Hexagon is composed of 6 equilateral triangles of side 12in, or 12 right-angled triangles, in this case with sides 6, 12 and 19. Two of these make a rectangle 6 x 19 ie 114 sqin. there are 6 such rectangles so the total area is 684 sqin. The only problem is that no such hexagon is possible, as the side must be greater than the apothem to satisfy Pythagoras?
How do you calculate the area of the polygon?
If it is a regular polygon--meaning that all the sides are congruent and all the angles are congruent, then the formula for area of the polygon is A=1/2 ap Here a represents the apothem, which is the distance from the center of the polygon to the midpoint of one side. p represents the perimeter of the polygon found by multiplying one side length by the number of sides. If you only know one variable such as side length, you can find the perimeter and you can find the apothem using trigonomety.
How do you find the area of a octagon with only the apothem?
Octagon is composed of 8 triangles, which can be combined in pairs to make 8 rectangles of which one side is the apothem. The area is 1.657 x the square of the apothem, simplified from 4 times the square of the apothem divided by tan67.5o ie 2.4142. 4 divided by 2.4142 is 1.657. Consider triangle OAB where OB is the apothem and AB is half of a side: The angle OAB = 67.5 degrees, half of the interior angle of a regular hexagon. Tan 67.5 = OB/AB so AB = OB/tan 67.5 and the area of each notional rectangle is OB squared divided by tan 67.5. There are four such rectangles hence 4OB2/tan 67.5 is the area of the octagon.
What is the area of a hexagon if one side is 5cm?
It is not possible to answer a question given only the length of one side of a hexagon unless we are told it is a regular hexagon. I added a link that lets you calculate areas of regular polygons.
What kinds of hexagon?
there is only one hexagon.
What is the area of a regular hexagon with an apothem of 16.5 yards long and a side 19 yards long rounded to the nearest tenth?
16.5
How do I find the diameter of a circle only having an arc length?
If you have only the arc length then you cannot find the diameter.
How do you find the perimeter of a hexagon if the area is given?
In general you cannot find the perimeter of any shape if only the area is given.
