GMAT Math : Polygons

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Example Questions

Example Question #2 : Calculating The Length Of A Side Of A Polygon

The perimeter of a regular pentagon is three kilometers. Give its sidelength in meters.

Possible Answers:

$50 \textrm{ m}$

$600 \textrm{ m}$

$375 \textrm{ m}$

$500 \textrm{ m}$

$60 \textrm{ m}$

Correct answer:

$600 \textrm{ m}$

Explanation:

One kilometer is equal to 1,000 meters, so two kilometers comprise 3,000 meters. A regular pentagon has five sides of equal length, so divide by 5 to get the sidelength: $3,000 \div 5 = 600$ meters.

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Example Question #5 : Calculating The Length Of A Side Of A Polygon

Six regular polygons each have perimeter one mile. The polygons are an equilateral triangle, a square, a pentagon, a hexagon, an octagon, and a decagon (ten-sided polygon). What is the mean of their sidelengths?

Possible Answers:

$1,240 \textrm{ ft}$

$1,320\textrm{ ft}$

$1,056 \textrm{ ft }$

$1,034\textrm{ ft}$

$880\textrm{ ft}$

Correct answer:

$1,034\textrm{ ft}$

Explanation:

The sidelength of a regular polygon is the perimeter of one mile, or 5,280 feet, divided by the number of sides. Therefore, the sidelengths of the six shapes are:

Triangle: $5,280 \div 3 = 1,760 \textrm{ ft}$

Square: $5,280 \div 4 = 1,320 \textrm{ ft}$

Pentagon: $5,280 \div 5 = 1,056 \textrm{ ft}$

Hexagon: $5,280 \div 6 = 880 \textrm{ ft}$

Octagon: $5,280 \div 8 = 660 \textrm{ ft}$

Decagon: $5,280 \div 10 = 528 \textrm{ ft}$

The mean of the six sidelengths:

$(1,760+1,320+1,056+880+660+528 ) \div 6 = 1,034$ feet

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Example Question #6 : Calculating The Length Of A Side Of A Polygon

If the shape $\textup{ABCDEF}$ is a regular hexagon with side length of 2x+6 and a perimeter of meters, what is the length of one side?

Possible Answers:

$3\ \textup{meters}$

$15\ \textup{meters}$

$5\ \textup{meters}$

$9\ \textup{meters}$

$12\ \textup{meters}$

Correct answer:

$12\ \textup{meters}$

Explanation:

Perimeter is the total distance around a shape. Here we have a regular (all sides are equal) hexagon with side distance 2x+6. Multiplying this expression by 6 gives us our perimeter.

$\small 72=6*(2x+6)=12x+36$

$\small 72-36=12x$

$\small 12x=36$

$\small x=3$

But we are not done yet. We need to plug this back in to get the side length

$\small 2(3)+6=9+6=15$

so 15 meters

Alternatively, we could divide 72 by 6 to get 12 meters.

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Example Question #3 : Calculating The Length Of A Side Of A Polygon

A regular hexagon has perimeter $2^{N}$ . Which of the following is equal to the length of one side?

Possible Answers:

$2^{\frac{N}{6}}$

$2^{N - 6}$

$3^{-N}$

$3 \cdot 2 ^{N-2}$

$\frac{2^{N-1} }{ 3}$

Correct answer:

$\frac{2^{N-1} }{ 3}$

Explanation:

A hexagon has six sides of equal length, so divide the perimeter by 6, which is the product of 2 and 3:

$\frac{2^{N}}{6} = \frac{2^{N}}{2 \cdot 3} = \frac{2^{N}}{2^{1} \cdot 3} = \frac{2^{N-1} }{ 3}$

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Example Question #4 : Calculating The Length Of A Side Of A Polygon

A regular octagon has perimeter $2^{N}$ . Give the length of one of its sides.

Possible Answers:

$2^{N -1}$

$2^{ \frac{1}{2}N}$

$2^{N -3}$

$2^{N -2}$

$2^{ \frac{1}{3}N}$

Correct answer:

$2^{N -3}$

Explanation:

A regular octagon has eight sides of equal length, so divide the perimeter by 8, or equivalently, $2^{3}$ :

$\frac{2^{N}}{2^{3}} = 2^{N-3}$ .

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GMAT Math : Polygons

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Calculating The Length Of A Side Of A Polygon

Example Question #5 : Calculating The Length Of A Side Of A Polygon

Example Question #6 : Calculating The Length Of A Side Of A Polygon

Example Question #3 : Calculating The Length Of A Side Of A Polygon

Example Question #4 : Calculating The Length Of A Side Of A Polygon

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