Chapter 12, Problem 35RE

To determine

To find: Number of tiles required for mosaic tile floor.

Answer to Problem 35RE

The number of tiles required for mosaic tile flooris 169.

Explanation of Solution

Given:

A mosaic tile floor is designed in the shape of a trapezoidal 30 feet wide at the base and 15 feet wide at the bottom. Tiles 12 inches by 12 inches are to be used.

Calculation:

Since,

  $\tan \theta =\frac{perpendicluar}{base}$

Therefore,

  $\begin{array}{l}\Rightarrow \tan {45}^{\circ }=\frac{perpendicluar}{7.5}\\ \Rightarrow perpendicluar=7.5\text{ feet}\end{array}$

Area of the trapezoidal,

  $\begin{array}{l}=\frac{1}{2}\left(15+30\right)\times 7.5\\ =168.75sq.ft.\end{array}$

Area of 1 tile,

  $\begin{array}{l}=1\times 1\\ =1sq.ft.\end{array}$

Therefore,

Number of tiles required,

  $\begin{array}{l}=\frac{168.75}{1}\\ =168.75\\ \approx 169\text{ tiles}\end{array}$

Hence,the number of tiles required for mosaic tile floor is 169.