What is the approximate area of the hexagon?
Understand the Problem
The question is asking for the approximate area of a hexagon. To solve this, we need to know the formula for the area of a hexagon and possibly the length of its sides or other provided measurements.
Answer
The approximate area of the hexagon is $A \approx 41.57$.
Answer for screen readers
The approximate area of the hexagon is $A \approx 41.57$ square units.
Steps to Solve
- Identify the area formula for a hexagon
The area of a regular hexagon can be calculated using the formula: $$ A = \frac{3\sqrt{3}}{2} s^2 $$ where $A$ is the area and $s$ is the length of a side.
- Plug in the side length
If we are given the side length (e.g., let’s assume $s = 4$), we will substitute this value into the area formula: $$ A = \frac{3\sqrt{3}}{2} (4)^2 $$
- Calculate the square of the side length
Now, calculate the square of the side length: $$ 4^2 = 16 $$
- Substitute and simplify
Substituting $16$ back into the area formula: $$ A = \frac{3\sqrt{3}}{2} \times 16 $$
- Perform the multiplication
Now multiply: $$ A = 24\sqrt{3} $$
- Find the approximate numerical value
Using the approximate value of $\sqrt{3} \approx 1.732$: $$ A \approx 24 \times 1.732 \approx 41.568 $$
The approximate area of the hexagon is $A \approx 41.57$ square units.
More Information
The area formula for a regular hexagon is derived from dividing it into 6 equilateral triangles. This makes it easier to understand how the area relates to the side length.
Tips
- Forgetting to square the side length before multiplying. Always ensure that you compute $s^2$ correctly.
- Confusing the side length with the apothem. Make sure to use the correct measurements based on the given problem.
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