George wants to paint a rectangular wall in his bedroom. He estimates that the wall has an area of 12 square meters.

In fact, the wall is 3.45 m long and 3.99 m high.

Calculate the percentage error in George's estimate, correct to 3 significant figures.

The problem involves finding the percentage error in George's estimate for the area of a rectangular wall. Let's break down the solution step by step.

### Step 1: Calculate the Actual Area of the Wall

The actual dimensions of the wall are:
- Length: \( 3.45 \, \text{m} \)
- Height: \( 3.99 \, \text{m} \)

The actual area is given by:

\[
\text{Actual Area} = \text{Length} \times \text{Height} = 3.45 \times 3.99
\]

\[
\text{Actual Area} = 13.7555 \, \text{m}^2
\]

### Step 2: Calculate the Error in George’s Estimate

George’s estimated area is \( 12 \, \text{m}^2 \).

The error in his estimate is the difference between the actual area and the estimated area:

\[
\text{Error} = \text{Actual Area} - \text{Estimated Area} = 13.7555 - 12 = 1.7555 \, \text{m}^2
\]

### Step 3: Calculate the Percentage Error

The percentage error is calculated using the formula:

\[
\text{Percentage Error} = \left( \frac{\text{Error}}{\text{Actual Area}} \right) \times 100
\]

Substituting the values:

\[
\text{Percentage Error} = \left( \frac{1.7555}{13.7555} \right) \times 100 \approx 12.76\%
\]

### Step 4: Round the Answer to 3 Significant Figures

The percentage error, correct to 3 significant figures, is:

\[
\boxed{12.8\%}
\]

Would you like more details or have any questions?

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Here are 5 related questions to consider:

1. How do you determine the correct number of significant figures in a calculation?
2. If George also underestimated the height of the wall, how would that affect the percentage error?
3. How can we calculate percentage error when the error is negative (underestimation)?
4. What other types of errors can occur in estimating areas or volumes?
5. How would the percentage error change if George's estimate was closer to the actual area?

**Tip:** Always round off your final answer only at the end of calculations to maintain accuracy.

Learn how to calculate the percentage error in George's estimate of a rectangular wall's area. George estimated the area at 12 square meters, but the actual dimensions are 3.45 meters long and 3.99 meters high. Discover the step-by-step solution using the area formula and percentage error calculation. Suitable for Grades 7-9.

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