/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 Find the area of a regular hexag... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 35

Find the area of a regular hexagon with sides of length \(s\).

Short Answer

Expert verified
The area of a regular hexagon with sides of length \(s\) can be found by dividing it into six equilateral triangles and calculating their total area. This can be done using the formula: \[Hexagon \, Area = 6 \times (\frac{\sqrt{3}}{4}s^2)\]

Step by step solution

01

Identify the formula for the area of an equilateral triangle

The formula for the area of an equilateral triangle with a side length \(s\) is: \[A = \frac{\sqrt{3}}{4}s^2\]
02

Calculate the area of one equilateral triangle

Substitute the given value of side length \(s\) in the formula: \[A = \frac{\sqrt{3}}{4}s^2\] Calculate the area of one equilateral triangle.
03

Calculate the area of a hexagon

Since a regular hexagon can be divided into six equilateral triangles, multiply the area of one equilateral triangle by six: \[Hexagon \, Area = 6 \times A \] After solving the above steps, you will get the area of a regular hexagon with sides of length \(s\).

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