Question

Case #4 TileThe diagram shows the design of a tile border around arectangular swimming pool that measures 7 meters by4 meters. Each tile is a square measuring 1 meter oneach side.a. What is the area of the pool?b. What is the area of both the pool and the tiles?c. Explain a method you couldjust the tiles.use to find the area of

Answer 1

a. The area of the pool is;

`A_1=28\text{ }m^2`

b. The area of both the pool and the tiles is;

`A_2=88\text{ }m^2`

c. The area of just the tiles is;

`A=60\text{ }m^2`

Step-by-step explanation:

a.

Given that the dimension of the pool is 7 meters by 4 meters.

`\begin{gathered} l=7\text{ m} \\ w=4\text{ m} \end{gathered}`

Recall that the area of a rectangle equals the product of the length and the width;

`A=l* w`

Substituting the given values;

`\begin{gathered} A_1=7*4 \\ A_1=28\text{ }m^2 \end{gathered}`

The area of the pool is;

`A_1=28\text{ }m^2`

b.

We can also calculate the area of the whole space including the tiles and the pool.

The dimension has 11 tiles by 8 tiles. since 1 tile has a length of 1 m.

The dimension of the whole area is 11 m by 8 m;

`\begin{gathered} l=11m \\ w=8m \end{gathered}`

applying the formula for the area of a rectangle we have;

`\begin{gathered} A=l* w \\ A_2=11*8 \\ A_2=88\text{ }m^2 \end{gathered}`

The area of both the pool and the tiles is;

`A_2=88\text{ }m^2`

c.

To calculate the area of just the tiles, we will apply the area subtraction method.

The area of just the tiles is equal to the area of both the tiles and pool minus the area of the pool;

`A=A_2-A_1`

substituting the values in a and b above;

`\begin{gathered} A=88m^2-28m^2 \\ A=60\text{ }m^2 \end{gathered}`

The area of just the tiles is;

`A=60\text{ }m^2`