$\"\"$

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To find the area(A) of the hexagon,you must find the apothem.

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Apothem: The central angles of a regular hexagon areall congruent. Therefore,

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the measure of each angle is $\"\"$ .

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Let GH is an apothem of hexagon ABCDEF. It bisects ∠DGH and is a perpendicular

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bisector of ED. So, m∠DGH = $\"\"$ . $\"\"$

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Since the perimeter(P) is 42 yards, each side is 7 yards and HD = 3.5 yards.

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Write a trigonometric ratio to find the length of GH.

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$\"\"$ ( $\"\"$ )

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Use a calculator $\"\"$ )

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$\"\"$

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$\"\"$ (Simplify) $\"\"$

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Area:

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Area of hexagon $\"\"$

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Where P is perimeter and a is apothem.

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$\"\"$ (Area of regular hexagon)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Multiply: $\"\"$ )

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$\"\"$ (Divide: $\"\"$ ) $\"\"$

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The value of area of hexagon $\"\"$ square yards.