To find the area of the hexagon, we can break it down into simpler shapes.
Step 1: Understand the shape
A regular hexagon can be divided into 6 identical equilateral triangles that all meet at the center.
Step 2: Identify the side length
The image shows that the distance from the center to a corner (the radius) is 1 inch. In a regular hexagon, this distance is equal to the length of the outer sides. So, we have 6 equilateral triangles, each with a side length ($s$) of 1 inch.
Step 3: Calculate the area of one triangle
The formula for the area of an equilateral triangle is:
$$ \text{Area} = \frac{\sqrt{3}}{4} \times s^2 $$
Since $s = 1$:
$$ \text{Area} = \frac{\sqrt{3}}{4} \times 1^2 $$
$$ \text{Area} = \frac{\sqrt{3}}{4} \text{ square inches} $$
Step 4: Calculate the total area
Since there are 6 triangles in the hexagon, we multiply the area of one triangle by 6:
$$ \text{Total Area} = 6 \times \frac{\sqrt{3}}{4} $$
$$ \text{Total Area} = \frac{6\sqrt{3}}{4} $$
We can simplify the fraction $\frac{6}{4}$ to $\frac{3}{2}$:
$$ \text{Total Area} = \frac{3\sqrt{3}}{2} \text{ square inches} $$
If you need a decimal approximation:
$\sqrt{3} \approx 1.732$
$$ \text{Total Area} \approx \frac{3 \times 1.732}{2} \approx \frac{5.196}{2} \approx 2.598 \text{ sq inches} $$
Final Answer:
The exact area is
$\frac{3\sqrt{3}}{2}$ square inches (or approximately
2.60 square inches).
Parent Tip: Review the logic above to help your child master the concept of printable graph paper hexagon.
