PSAT Math help » Geometry » airplane Geometry » Hexagons » how to discover the length of the diagonal line of a hexagon

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*


*


*


Explanation:

A diagonal is a heat segment joining two non-adjacent vertices the a polygon. A consistent hexagon has six sides and also six vertices. One vertex has three diagonals, for this reason a hexagon would have three diagonals times 6 vertices, or 18 diagonals. Division this number through 2 come account for duplicate diagonals in between two vertices. The formula because that the variety of vertices in a polygon is:

*

where

*
.

You are watching: How many diagonals in a hexagon


Explanation:

A diagonal line connects two non-consecutive vertices the a polygon. A hexagon has six sides. There room 3 diagonals native a single vertex, and also there are 6 vertices on a hexagon, which suggests there would certainly be 18 diagonals in a hexagon. However, we need to divide by 2 as fifty percent of the diagonals are typical to the exact same vertices. For this reason there room 9 unique diagonals in a hexagon. The formula for the number of diagonals of a polygon is:

*

where n = the variety of sides in the polygon.

Thus a pentagon thas 5 diagonals. An octagon has 20 diagonals.


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Example question #1 : Hexagons


Regular Hexagon  has a diagonal 

*
 with length 1.

Give the size of diagonal 

*


Possible Answers:
Correct answer:

*


Explanation:

The an essential is come examine  in thie figure below:

Each inner angle that a regular hexagon, including 

*
, measures 
*
, so it deserve to be conveniently deduced by means of the Isosceles Triangle organize that 
*
*
, therefore by edge addition, 

*
.

Also, through symmetry,

*
,

so 

*
,

and  is a  triangle whose long leg 

*
 has length 
*
.

By the  Theorem,

*
, i beg your pardon is the hypotenuse of , has actually length 
*
 times the of the long leg, so 
*
.


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Example inquiry #1 : just how To discover The size Of The diagonal Of A Hexagon


Regular Hexagon  has a diagonal 

*
 with length 1.

Give the size of diagonal 

*


Possible Answers:
Correct answer:

*


Explanation:

The an essential is come examine  in thie figure below:

Each internal angle the a constant hexagon, including 

*
, measures 
*
, therefore it deserve to be easily deduced by means of the Isosceles Triangle organize that 
*
*
, so by edge addition, 

*
.

Also, through symmetry,

*
,

so 

*
,

and  is a  triangle who hypotenuse 

*
 has length 
*
.

By the  Theorem, the lengthy leg 

*
 of  has length 
*
 times the of hypotenuse 
*
, so 
*
.


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Example concern #3 : Hexagons


Regular hexagon  has side size of 1.

Give the length of diagonal 

*


Possible Answers:
Correct answer:

*


Explanation:

The key is come examine  in thie number below:

Each internal angle the a constant hexagon, consisting of

*
, measures 
*
, therefore it have the right to be conveniently deduced by method of the Isosceles Triangle theorem that . To find
*
 we can subtract  from 
*
. Thus resulting in:

*

Also, through symmetry,

*
,

so 

*
.

Therefore, 

*
 is a  triangle whose brief leg
*
 has size
*
.

The hypotenuse

*
 of this  triangle steps twice the size of short leg
*
, so 
*
.


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Example concern #4 : Hexagons


Regular hexagon  has side length 1.

Give the size of diagonal 

*


Possible Answers:
Correct answer:

*


Explanation:

The crucial is come examine  in thie figure below:

Each internal angle the a consistent hexagon, including 

*
, measures 
*
, for this reason it have the right to be conveniently deduced by means of the Isosceles Triangle theorem that 
*
. To find 
*
 we subtract
*
 from
*
. Therefore resullting in 
*

Also, through symmetry,

*
,

so 

*
,

and 

*
 is a  triangle whose short leg
*
 has length 
*
.

See more: How Many Slices Does A Large Pizza Have, How Many Slices Are In A Large Pizza

The lengthy leg 

*
 of this  triangle steps
*
 times the size of quick leg
*
, so 
*
.


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