Given:
A regular hexagon with side 11.5 units and apothem 10 units.
To find:
The area round to the nearest tenth.
Solution:
Area of a regular polygon is:
[tex]A=\dfrac{1}{2}Pa[/tex] ...(i)
Where, P is the perimeter and a is the apothem.
The given figure is a regular hexagon with six sides. So, the perimeter of the given figure is the product of number of sides and the side length.
[tex]P=6\times 11.5[/tex]
[tex]P=69[/tex]
Putting [tex]P=69,a=10[/tex], we get
[tex]A=\dfrac{1}{2}(69)(10)[/tex]
[tex]A=(69)(5)[/tex]
[tex]A=345
[/tex]
Therefore, the area of the regular polygon is 345.0 square units.
