What is the area of a regular hexagon with a 48-inch perimeter?

Answer 1

#16 sqrt(3) approx 27.71# square inches.

First of all, if the perimeter of a regular hexagon measures #48# inches, then each of the #6# sides has to be #48/6=8# inches long.

To compute the area, you can divide the figure in equilateral triangles as follows.

Given the side #s#, the area of an equilateral triangle is given by #A=sqrt(3)/4 s^2# (you can prove this using the Pythagorean Theorem or trigonometry).

In our case #s=8# inches, so the area is #A=sqrt(3)/4 8^2=16 sqrt(3) approx 27.71# square inches.

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Answer 2

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

Area = (3√3 * side length^2) / 2

Given the perimeter of the hexagon is 48 inches, divide by 6 to find the length of each side:

48 inches ÷ 6 = 8 inches

Substitute the side length into the formula:

Area = (3√3 * 8 inches^2) / 2

Area = (3√3 * 64 square inches) / 2

Area = (192√3 square inches) / 2

Area = 96√3 square inches

So, the area of the regular hexagon with a 48-inch perimeter is 96√3 square inches.

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Answer from HIX Tutor

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.

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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