A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. What is the approximate area of the hexagon?
A. $224 cm^2$
B. $336 cm^2$
C. $448 cm^2$
D. $672 cm^2$
Answer (1)
The problem provides the apothem and perimeter of a regular hexagon.
The area of the hexagon is calculated using the formula: Area = 2 1 × apothem × perimeter .
Substituting the given values, Area = 2 1 × 14 cm × 96 cm .
The approximate area of the hexagon is 672 cm 2 .
Explanation
Problem Analysis We are given a regular hexagon with an apothem of 14 cm and a perimeter of approximately 96 cm. Our goal is to find the approximate area of this hexagon.
Area Formula The area of a regular polygon can be calculated using the formula:
Area = 2 1 × apothem × perimeter
Substitution Now, we substitute the given values into the formula:
Area = 2 1 × 14 cm × 96 cm
Calculation Performing the calculation:
Area = 7 cm × 96 cm
Area = 672 cm 2
Final Answer Therefore, the approximate area of the hexagon is 672 cm 2 .
Examples
Imagine you are designing a hexagonal garden bed and need to calculate the area to determine how much soil to purchase. Knowing the apothem (the distance from the center to the midpoint of a side) and the perimeter allows you to quickly estimate the area using the formula: Area = (1/2) * apothem * perimeter. This calculation helps you plan your gardening project efficiently, ensuring you have enough materials to fill the space.
