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A regular hexagon has an apothem of 14. 7 inches and a perimeter of 101. 8 inches. What is the area of the hexagon?.

User Tsherwen
by
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1 Answer

3 votes

Answer:

748.23 in²

Explanation:

Area of a Regular Polygon


\textsf{Area of a regular polygon}=(n\:l\:a)/(2)

where:

  • n = number of sides
  • l = length of one side
  • a = apothem

Given:

  • n = 6
  • l = 101.8 ÷ 6
  • a = 14.7

Substituting the given values into the formula and solving for A:


\implies \textsf{A}=(6 \cdot (101.8)/(6) \cdot 14.7)/(2)


\implies \sf A=(101.8 \cdot 14.7)/(2)


\implies \sf A=(1496.46)/(2)


\implies \sf A=748.23

Therefore, the area of the hexagon is 748.23 in²

User Igor Semenov
by
5.3k points