Questions: Find the missing dimension of the regular hexagon shown to the right. Round to the nearest whole number. The missing dimension is approximately

Find the missing dimension of the regular hexagon shown to the right. Round to the nearest whole number. The missing dimension is approximately
Transcript text: Find the missing dimension of the regular hexagon shown to the right. Round to the nearest whole number. The missing dimension is approximately $\square$
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Solution

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Solution Steps

Step 1: Identify the given information

The problem provides the apothem (154 units) of a regular hexagon and asks for the side length.

Step 2: Understand the relationship between the apothem and the side length

For a regular hexagon, the apothem (a) is related to the side length (s) by the formula: \[ a = \frac{s \sqrt{3}}{2} \]

Step 3: Rearrange the formula to solve for the side length

Rearrange the formula to solve for \( s \): \[ s = \frac{2a}{\sqrt{3}} \]

Step 4: Substitute the given apothem value into the formula

Substitute \( a = 154 \) into the formula: \[ s = \frac{2 \times 154}{\sqrt{3}} \]

Step 5: Calculate the side length

Perform the calculation: \[ s = \frac{308}{\sqrt{3}} \approx \frac{308}{1.732} \approx 177.8 \]

Step 6: Round to the nearest whole number

Round 177.8 to the nearest whole number: \[ s \approx 178 \]

Final Answer

The missing dimension is approximately 178 units.

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