Problem

$69^{\circ}$
30. Calculate the area of a regular hexagon with side lengths 1 feet and an apothem of $3 \sqrt{10}$ feet.
$9 \sqrt{10}$ square units
$4 \sqrt{10}$ square units
$7.5 \sqrt{10}$ square units
not enough information

Answer

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Answer

The area of the regular hexagon is approximately \(\boxed{28.46}\) square feet. However, this is not one of the options given in the question.

Steps

Step 1 :Given a regular hexagon with side lengths 1 feet and an apothem of \(3 \sqrt{10}\) feet.

Step 2 :The area of a regular hexagon can be calculated using the formula: Area = \(\frac{1}{2} \times \text{Perimeter} \times \text{Apothem}\).

Step 3 :The perimeter of a regular hexagon with side length 1 is 6 (since a hexagon has 6 sides).

Step 4 :Substitute these values into the formula to find the area.

Step 5 :The area of the regular hexagon is approximately \(\boxed{28.46}\) square feet. However, this is not one of the options given in the question.

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