Answer:
[tex]\large\boxed{a)\ A\approx93.53\ in^2}\\\boxed{b)\ 8,640\ in^2}[/tex]
Step-by-step explanation:
a)
The formula of an area of a regular hexagon:
[tex]A=6\cdot\dfrac{a^2\sqrt3}{4}[/tex]
a - side length
We have a = 6in. Substitute:
[tex]A=6\!\!\!\!\diagup^3\cdot\dfrac{6^2\sqrt3}{4\!\!\!\!\diagup_2}=3\cdot\dfrac{36\!\!\!\!\!\diagup^{18}\sqrt3}{2\!\!\!\!\diagup_1}=3\cdot18\sqrt3=54\sqrt3\ in^2\\\\A\approx93.53\ in^2[/tex]
b)
[tex]5ft=5(12in)=60in\\\\12ft=(12)(12in)=144in[/tex]
The area of a hallway:
[tex]A=(60)(144)=8,640\ in^2[/tex]
