Answer :
The area of a regular hexagon with an apothem 13 inches long and a side 15 inches long is 1,169 in² (option d).
A regular hexagon is a polygon with six equal sides and six equal angles. The apothem of a regular polygon is the perpendicular distance from the center of the polygon to one of its sides. The side length of a regular hexagon is the distance between two consecutive vertices.
In this problem, we are given the apothem, which is 13 inches long, and the side length, which is 15 inches long. To find the area of the regular hexagon, we can use the formula:
Area = (3 × side length × apothem) / 2
Substituting the given values into the formula, we get:
Area = (3 × 15 × 13) / 2
Area = (45 × 13) / 2
Area ≈ 1,169 in²
Therefore, the correct answer is option (d) 1,169 in².
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