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

Answer:

748.23 in²

Step-by-step explanation:

Area of a Regular Polygon

$\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}$

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:

$\implies \textsf{A}=\dfrac{6 \cdot \dfrac{101.8}{6} \cdot 14.7}{2}$

$\implies \sf A=\dfrac{101.8 \cdot 14.7}{2}$

$\implies \sf A=\dfrac{1496.46}{2}$

$\implies \sf A=748.23$

Therefore, the area of the hexagon is 748.23 in²