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ACT Math : How to find the perimeter of a hexagon

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Example Question #1 : How To Find The Perimeter Of A Hexagon

Hexcenter431

The figure above is a regular hexagon. is the center of the figure. The line drawn is perpendicular to the side.

What is the perimeter of the figure above?

Possible Answers:

$4\sqrt{3}$

$48\sqrt{3}$

Correct answer:

Explanation:

You can redraw the figure given to notice the little equilateral triangle that is formed within the hexagon. Since a hexagon can have the 360 degrees of its internal rotation divided up evenly, the central angle is degrees. The two angles formed with the sides also are degrees. Thus, you could draw:

Hexcenter432

Now, the $4\sqrt{3}$ is located on the side that is the same as $\sqrt{3}$ on your standard 30-60-90 triangle. The base of the little triangle formed here is on the standard triangle. Let's call our unknown value .

We know, then, that:

$\frac{4\sqrt{3}}{\sqrt{3}}=\frac{x}{1}$

Or, x=4

Now, this is only half of the size of the hexagon's side. Therefore, the full side length is 4*2=8 .

Since this is a regular hexagon, all of the sides are of equal length. This means that your total perimeter is 8*6 or .

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Example Question #1 : Hexagons

What is the perimeter of a regular hexagon with an area of $315.375\sqrt{3}\:units^2$ ?

Possible Answers:

$157.6875\:units$

$87\:units$

$157.6875\sqrt{3}\:units$

$92\:units$

$78\sqrt{3}\:units$

Correct answer:

$87\:units$

Explanation:

The area of a regular hexagon is defined by the equation:

$\frac{3\sqrt{3}}{2} * s^2$ , where is the length of a side.

This is derived from the fact that the regular hexagon can be split up into little equilateral triangles, each having an area of

$\frac{\sqrt{3}}{4}*s^2$

To visualize this, consider the drawing:

Hexagontriangle

Each triangle formed like this will be equilateral. It is easiest to remember this relationship and memorize the general area equation for equilateral triangles. (It is useful in many venues!)

So, for your data, you know:

$315.375\sqrt{3}=\frac{3\sqrt{3}}{2} * s^2$

Solving for , you get:

s^2 = 210.25

This means that s=14.5

Therefore, the perimeter of the figure is equal to 6*s or $87\:units$ .

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Example Question #1 : Hexagons

Find the perimeter of a hexagon with a side length of .

Possible Answers:

Correct answer:

Explanation:

There are 6 sides in a hexagon.

Therefore, given a side length of 16, the perimeter is:

$P=6s=6 \cdot 16=96$

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Example Question #2 : How To Find The Perimeter Of A Hexagon

The side length of a hexagon is $\frac{x}{3}$ . What is the perimeter?

Possible Answers:

$\frac{6x+6}{3}$

$\frac{x+6}{6}$

$\frac{x+6}{3}$

x+6

Correct answer:

Explanation:

Write the formula for the perimeter of a hexagon.

P=6s

Substitute the given length.

$P=6s = 6\left(\frac{x}{3}\right)=2x$

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ACT Math : How to find the perimeter of a hexagon

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Hexagon

Example Question #1 : Hexagons

Example Question #1 : Hexagons

Example Question #2 : How To Find The Perimeter Of A Hexagon

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