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Example Questions
Example Question #2 :How To Find The Length Of The Diagonal Of A Hexagon
How many diagonals are there in a regular hexagon?
A diagonal is a line segment joining two non-adjacent vertices of a polygon. A regular hexagon has six sides and six vertices. One vertex has three diagonals, so a hexagon would have three diagonals times six vertices, or 18 diagonals. Divide this number by 2 to account for duplicate diagonals between two vertices. The formula for the number of vertices in a polygon is:
where.
Example Question #3 :How To Find The Length Of The Diagonal Of A Hexagon
How many diagonals are there in a regular hexagon?
9
18
3
10
6
9
A diagonal connects two non-consecutive vertices of a polygon. A hexagon has six sides. There are 3 diagonals from a single vertex, and there are 6 vertices on a hexagon, which suggests there would be 18 diagonals in a hexagon. However, we must divide by two as half of the diagonals are common to the same vertices. Thus there are 9 unique diagonals in a hexagon. The formula for the number of diagonals of a polygon is:
where n = the number of sides in the polygon.
Thus a pentagon thas 5 diagonals. An octagon has 20 diagonals.
Example Question #1 :Hexagons
Regular Hexagonhas a diagonalwith length 1.
Give the length of diagonal.
The key is to examinein thie figure below:
Each interior angle of a regular hexagon, including, measures, so it can be easily deduced by way of the Isosceles Triangle Theorem that., so by angle addition,
.
Also, by symmetry,
,
so,
andis atriangle whose long leghas length.
By theTheorem,, which is the hypotenuse of, has lengthtimes that of the long leg, so.
Example Question #2 :Hexagons
Regular Hexagonhas a diagonalwith length 1.
Give the length of diagonal.
The key is to examinein thie figure below:
Each interior angle of a regular hexagon, including, measures, so it can be easily deduced by way of the Isosceles Triangle Theorem that., so by angle addition,
.
Also, by symmetry,
,
so,
andis atriangle whose hypotenusehas length.
By theTheorem, the long legofhas lengthtimes that of hypotenuse, so.
Example Question #3 :Hexagons
Regular hexagonhas side length of 1.
Give the length of diagonal.
The key is to examinein thie figure below:
Each interior angle of a regular hexagon, including, measures, so it can be easily deduced by way of the Isosceles Triangle Theorem that. To findwe can subtractfrom. Thus resulting in:
Also, by symmetry,
,
so.
Therefore,is atriangle whose short leghas length.
The hypotenuseof thistriangle measures twice the length of short leg, so.
Example Question #4 :Hexagons
Regular hexagonhas side length 1.
Give the length of diagonal.
The key is to examinein thie figure below:
Each interior angle of a regular hexagon, including, measures, so it can be easily deduced by way of the Isosceles Triangle Theorem that. To findwe subtractfrom. Thus resullting in
Also, by symmetry,
,
so,
andis atriangle whose short leghas length.
The long legof thistriangle measurestimes the length of short leg, so.
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