Question

A floor tile is In the shape of a rectangular hexagon Greg uses 187.5 floor tiles for a room the area of the room is 450 ft.² find the length of each side of the hexagon

Answer 1

Answer:

The length of each side of Floor tile is 0.961 ft.

Step-by-step explanation:

Given:

A floor tile is In the shape of a regular hexagon

Area Of Room = $450\ ft^2$

Number of tiles used = 187.5

we need to find the length of each side of the hexagon.

First we will find the area of floor tiles.

Area of floor tiles is calculated by dividing Area Of Room with Number of tiles used.

Framing in equation form we get;

Area of Floor tiles = $\frac{450}{187.5}= 2.4\ ft^2$

Now we will find the length of each side of hexagon;

Now Area of Regular hexagon = $\frac{3\sqrt{3}}{2}a^2$

Now Substituting the values we get;

$2.4 = \frac{3\sqrt{3}}{2}a^2\\\\2.4\times 2=3\sqrt{3}\times a^2 \\\\4.8 = 3\times 1.732\times a^2\\\\4.8 = 5.196 a^2\\\\a^2=\frac{4.8}{5.196} \\\\a^2= 0.923\\\\a=\sqrt{0.923} = 0.961\ ft$

Hence the length of each side of Floor tile is 0.961 ft.