PSAT Math : How to find the length of the side of a hexagon

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #581 : Geometry

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above hexagon is 888. Also, . Evaluate .

Possible Answers:

Insufficient information is given to answer the problem.

Correct answer:

Explanation:

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Along with , we now have a system of equations to solve for  by adding:

 

Example Question #1 : Hexagons

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 132. What is  ?

Possible Answers:

Correct answer:

Explanation:

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Example Question #3 : How To Find The Length Of The Side Of A Hexagon

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of  to  is . Evaluate 

Possible Answers:

Correct answer:

Explanation:

The perimeter of the figure can be expressed in terms of the variables by adding:

Simplify and set :

Since the ratio of  to  is equivalent to  - or

,

then 

and we can substitute as follows:

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