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EXAMPLE 3

Learn how to find the length of a side of a hexagonal table by solving algebraic expressions. Example and guided practice included.

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EXAMPLE 3

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  1. A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side. ALGEBRA 3x + 6 4x – 2 = 6 x – 2 = 8 x = EXAMPLE 3 Find side lengths SOLUTION First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent. Write equation. Subtract 3x from each side. Add 2 to each side.

  2. 3x + 6 3(8) + 6 = = 30 The length of a side of the table is 30inches. ANSWER EXAMPLE 3 Find side lengths Then find a side length. Evaluate one of the expressions when x = 8.

  3. 3. The expressions 8y° and ( 9y – 15 )° represent the measures of two of the angles in the table in Example 3. Find the measure of an angle. for Example 3 GUIDED PRACTICE SOLUTION First , write and solve an equation to find the value of y. Use the fact that that the angles of a regular hexagon are congruent. 8y = 9y – 15 Write equation 0 = y – 15 Subtract each side by 8y 15 = y Add 15 to each side

  4. ANSWER The measure of an angle is 120° for Example 3 GUIDED PRACTICE Then find an angle. Evaluate one the expression when y = 15° 8y = 8 · 15° = 120°

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