Answer:
748.23 in²
Explanation:
Area of a Regular Polygon
![\textsf{Area of a regular polygon}=(n\:l\:a)/(2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/d0petyvkox9sbad2qyro665x87n9cm5wfu.png)
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)](https://img.qammunity.org/2023/formulas/mathematics/high-school/swjurum3yaa567oephwzv2v5b8c7wzlzbi.png)
![\implies \sf A=(101.8 \cdot 14.7)/(2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/l8idjfv0nc8z4oqfcxx85mcqzrnqxzb3wc.png)
![\implies \sf A=(1496.46)/(2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/61vh76rdg2r1g5h0uw5v4iep8mbb6nr9qy.png)
![\implies \sf A=748.23](https://img.qammunity.org/2023/formulas/mathematics/high-school/dntwgzkeozsd6ciujksxqwyzeiq9z8g33c.png)
Therefore, the area of the hexagon is 748.23 in²