How to find the length of the side of a hexagon

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

Questions 1 - 3

1

Hexagon

Note: Figure NOT drawn to scale.

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

$16 \frac{1}{2}$

$26\frac{2}{5}$

Explanation

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

$A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P$

Simplify and set :

$6\left (A + B \right )= 132$

2

Hexagon

Note: Figure NOT drawn to scale.

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

Explanation

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

$A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P$

Simplify and set :

Since the ratio of to is equivalent to - or

$\frac{A}{B} = \frac{3}{2}$ ,

then

$A = \frac{3}{2} B$

and we can substitute as follows:

$6 \cdot \frac{3}{2}B + 6B= 600$

3

Hexagon

Note: Figure NOT drawn to scale.

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

$A = 93\frac{4}{5}$

$A = 60\frac{1}{2}$

Insufficient information is given to answer the problem.

Explanation

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

$A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P$

Simplify and set :

$6\left (A + B \right )= 888$

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

$\underline{A-B =; 10}$

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