MAT1793-ABED_1: Estimation Example 2

EXAMPLE 2

The wall separating the kitchen and dining room of a house has an arched doorway. As part of a renovation, travertine (stone) is going to be put on the entire surface of this wall. The travertine costs $79.75 per case, and each case covers 5 ft². Estimate the cost of travertine needed to cover the entire wall. Each square on the grid represents 1 ft².

Solution

Step 1: Underestimate the area of space inside the outline of the wall.

There are 128 full squares inside the outline of the wall. The underestimation is 128 ft².

Step 2: Overestimate the area of space touching the outline of the wall.

There are 206 full squares touching the wall. The overestimation is 206 ft².

Step 3: Calculate the average

$\begin{align} \text{A}_{\text{estimate}}&=\frac{\left(\text{underestimate + overestimate}\right)}{2} \\ \\ &=\frac{\left(128\,\text{ft}^2+206\,\text{ft}^2\right)}{2} \\ \\ &=167\,\text{ft}^2 \\ \end{align}$

The area is approximately 167 ft².

Step 4: Calculate the number of cases of travertine needed.

Each case covers 5 ft².

$\begin{align} \text{number of cases}&=\frac{167\,\text{ft}^2}{5\,\text{ft}^2/\text{case}} \\ \\ \\ &=33.4\,\text{cases} \\ \end{align}$

A total of 34 cases must be purchased.

The number of cases must be rounded up to 34 to avoid running out of building material (travertine).

Step 5: Calculate the cost of the travertine.

$\begin{align} \text{cost}&=34\,\text{cases}\times \$79.75 \\ \\ &=\$2711.50 \\ \end{align}$

The travertine for the wall will cost approximately $2 711.50.

Estimation Example 2

Lesson 2: Area - Estimation Example 2

EXAMPLE 2

Solution

Now, it is your turn! Complete the questions in your Chapter 7, Lesson 2 Practice Makes Perfect that refer to Area Estimation.