Question

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

Answer 1

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