# What is the area of a hexagon whose perimeter is 24 feet?

See a solution process below:

Assuming this is a regular hexagon (all 6 sides have the same length) then the formula for the perimeter of a hexagon is:

Substituting 24 feet for

Now we can use the value for

Substituting

or

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We need to assume that it is a regular hexagon - meaning that all the six sides and angles are equal,

A hexagon is the only polygon which is made up of equilateral triangles.

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To find the area of a regular hexagon, you can use the formula:

[ \text{Area} = \frac{3\sqrt{3}}{2} \times s^2 ]

Where ( s ) is the length of one side of the hexagon.

Given that the perimeter of the hexagon is 24 feet and it has 6 sides, each side's length is ( \frac{24}{6} = 4 ) feet.

Now, substitute ( s = 4 ) into the formula:

[ \text{Area} = \frac{3\sqrt{3}}{2} \times 4^2 ]

[ \text{Area} = \frac{3\sqrt{3}}{2} \times 16 ]

[ \text{Area} = 24\sqrt{3} ]

So, the area of the hexagon is ( 24\sqrt{3} ) square feet.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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