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 #2 : Hexagons

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above hexagon is 888. Also, \(\displaystyle A-B = 10\). Evaluate \(\displaystyle A\).

Possible Answers:

Insufficient information is given to answer the problem.

\(\displaystyle A = 93\frac{4}{5}\)

\(\displaystyle A = 79\)

\(\displaystyle A = 60\frac{1}{2}\)

\(\displaystyle A = 116\)

Correct answer:

\(\displaystyle A = 79\)

Explanation:

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

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

Simplify and set \(\displaystyle P = 888\):

\(\displaystyle A + A + 2A + 2A + B+ B +2B + 2B= 888\)

\(\displaystyle 6A + 6B= 888\)

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

\(\displaystyle A + B = 148\)

Along with \(\displaystyle A-B = 10\), we now have a system of equations to solve for \(\displaystyle A\) by adding:

\(\displaystyle A + B = 148\)

\(\displaystyle \underline{A-B =\; 10}\)

\(\displaystyle 2A = \; \; \; \; \; \; 158\)

\(\displaystyle A = 79\)

 

Example Question #3 : Hexagons

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 132. What is \(\displaystyle A + B\) ?

Possible Answers:

\(\displaystyle 22\)

\(\displaystyle 44\)

\(\displaystyle 33\)

\(\displaystyle 16 \frac{1}{2}\)

\(\displaystyle 26\frac{2}{5}\)

Correct answer:

\(\displaystyle 22\)

Explanation:

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

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

Simplify and set \(\displaystyle P = 132\):

\(\displaystyle A + A + 2A + 2A + B+ B +2B + 2B= 132\)

\(\displaystyle 6A + 6B= 132\)

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

\(\displaystyle A + B = 22\)

Example Question #7 : Hexagons

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of \(\displaystyle A\) to \(\displaystyle B\) is \(\displaystyle 3:2\). Evaluate \(\displaystyle B\)

Possible Answers:

\(\displaystyle B = 100\)

\(\displaystyle B = 40\)

\(\displaystyle B = 48\)

\(\displaystyle B = 60\)

\(\displaystyle B = 72\)

Correct answer:

\(\displaystyle B = 40\)

Explanation:

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

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

Simplify and set \(\displaystyle P = 600\):

\(\displaystyle A + A + 2A + 2A + B+ B +2B + 2B= 600\)

\(\displaystyle 6A + 6B= 600\)

Since the ratio of \(\displaystyle A\) to \(\displaystyle B\) is equivalent to \(\displaystyle 3:2\) - or

\(\displaystyle \frac{A}{B} = \frac{3}{2}\),

then 

\(\displaystyle A = \frac{3}{2} B\)

and we can substitute as follows:

\(\displaystyle 6 \cdot \frac{3}{2}B + 6B= 600\)

\(\displaystyle 9B + 6B= 600\)

\(\displaystyle 15B = 600\)

\(\displaystyle B = 40\)

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