Answer:
[tex]A=64.95\ in^2[/tex]
Step-by-step explanation:
we know that
A regular hexagon can be divided into six equilateral triangles
so
The area of a regular hexagon is the same that the area of six congruent equilateral triangles
The area of one equilateral triangle in the regular hexagon is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
b is the base of triangle (the length of the regular hexagon)
h is the height of triangle (the apothem of the regular hexagon)
so
[tex]b=5\ in\\h=4.33\ in[/tex]
substitute
[tex]A=\frac{1}{2}(5)(4.33)=10.825\ in^2[/tex]
Multiply the area of one triangle by 6 to obtain the area of the regular hexagon
[tex]A=10.825(6)=64.95\ in^2[/tex]
