A Rectangle Has Vertices At \[$(-3,2), (7,2), (7,-5)\$\], And \[$(-3,-5)\$\]. Jordan Says The Area Of The Rectangle Is 70 Square Units.$\[ \begin{tabular}{|c|c|} \hline Steps & Jordan's Work \\ \hline Step 1 & Base: \(|-3| + |7| =

Mar 1, 2025 by ADMIN 233 views

**A Rectangle's Area: Unraveling Jordan's Calculation**

Introduction

In mathematics, calculating the area of a rectangle is a fundamental concept that involves understanding the relationship between its length, width, and the formula for finding the area. Recently, Jordan attempted to calculate the area of a given rectangle with vertices at ${(-3,2), (7,2), (7,-5),}$ and ${(-3,-5)}$ . However, his calculation resulted in an area of 70 square units, which we will investigate and discuss in this article.

Understanding the Rectangle's Dimensions

To calculate the area of a rectangle, we need to determine its length and width. The length is the distance between two opposite sides, while the width is the distance between the other two opposite sides. In this case, the given vertices of the rectangle are ${(-3,2), (7,2), (7,-5),}$ and ${(-3,-5)}$ .

Calculating the Length

The length of the rectangle can be calculated by finding the distance between the points ${(-3,2)}$ and ${(7,2)}$ . This distance is given by the absolute difference between the x-coordinates of the two points, which is ${|7 - (-3)| = |7 + 3| = 10}$ units.

Calculating the Width

Similarly, the width of the rectangle can be calculated by finding the distance between the points ${(-3,2)}$ and ${(-3,-5)}$ . This distance is given by the absolute difference between the y-coordinates of the two points, which is ${|2 - (-5)| = |2 + 5| = 7}$ units.

Calculating the Area

Now that we have determined the length and width of the rectangle, we can calculate its area using the formula: Area = Length × Width. Substituting the values we found earlier, we get: Area = 10 × 7 = 70 square units.

Discussion

However, Jordan's calculation resulted in an area of 70 square units, which seems to be correct based on our calculation. But let's take a closer look at his work to see if there's anything we can learn from it.

Jordan's Work

Jordan's work is as follows:

Step 1: Base: ${|-3| + |7| = 10}$
Step 2: Height: ${|2 - (-5)| = 7}$
Step 3: Area: ${10 \times 7 = 70}$

Analyzing Jordan's Calculation

At first glance, Jordan's calculation seems correct. However, let's analyze it further to see if there's anything we can learn from it. In Step 1, Jordan correctly calculated the length of the rectangle by finding the distance between the points ${(-3,2)}$ and ${(7,2)}$ . This distance is indeed 10 units.

In Step 2, Jordan correctly calculated the width of the rectangle by finding the distance between the points ${(-3,2)}$ and ${(-3,-5)}$ . This distance is indeed 7 units.

In Step 3, Jordan correctly calculated the area of the rectangle by multiplying the length and width. This results in an area of 70 square units, which is indeed correct.

Conclusion

In conclusion, Jordan's calculation of the area of the rectangle is correct. However, it's always a good idea to double-check our work to ensure that we haven't made any mistakes. By analyzing Jordan's work, we can see that he correctly calculated the length and width of the rectangle and then used the formula to find the area.

Final Thoughts

Calculating the area of a rectangle is a fundamental concept in mathematics that involves understanding the relationship between its length, width, and the formula for finding the area. By following the steps outlined in this article, we can ensure that our calculations are accurate and reliable. Whether you're a student or a professional, understanding how to calculate the area of a rectangle is an essential skill that can be applied in a variety of real-world situations.

Additional Resources

For further reading on this topic, we recommend the following resources:

References

About the Author

Q&A: Calculating the Area of a Rectangle

Introduction

In our previous article, we explored the concept of calculating the area of a rectangle and applied it to a specific problem. However, we received many questions from readers who wanted to know more about the topic. In this article, we will address some of the most frequently asked questions about calculating the area of a rectangle.

Q: What is the formula for calculating the area of a rectangle?

A: The formula for calculating the area of a rectangle is: Area = Length × Width.

Q: How do I calculate the length of a rectangle?

A: To calculate the length of a rectangle, you need to find the distance between two opposite sides. This can be done by finding the absolute difference between the x-coordinates of the two points.

Q: How do I calculate the width of a rectangle?

A: To calculate the width of a rectangle, you need to find the distance between the other two opposite sides. This can be done by finding the absolute difference between the y-coordinates of the two points.

Q: What if the rectangle is not a perfect rectangle?

A: If the rectangle is not a perfect rectangle, you can still calculate its area by using the formula: Area = Length × Width. However, you need to make sure that you are using the correct values for the length and width.

Q: Can I use a calculator to calculate the area of a rectangle?

A: Yes, you can use a calculator to calculate the area of a rectangle. However, it's always a good idea to double-check your work to ensure that you haven't made any mistakes.

Q: What if I'm given the area of a rectangle and I need to find the length and width?

A: If you're given the area of a rectangle and you need to find the length and width, you can use the formula: Area = Length × Width. Rearranging the formula, you get: Length = Area ÷ Width. You can then use this formula to find the length and width of the rectangle.

Q: Can I use this formula to calculate the area of other shapes?

A: No, this formula is specifically designed for calculating the area of rectangles. However, there are other formulas that you can use to calculate the area of other shapes, such as triangles, circles, and polygons.

Q: What if I'm not sure how to calculate the area of a rectangle?

A: If you're not sure how to calculate the area of a rectangle, don't worry! You can always ask a teacher, tutor, or online resource for help. There are many resources available that can provide you with step-by-step instructions and examples.

Conclusion

Calculating the area of a rectangle is a fundamental concept in mathematics that involves understanding the relationship between its length, width, and the formula for finding the area. By following the steps outlined in this article, you can ensure that your calculations are accurate and reliable. Whether you're a student or a professional, understanding how to calculate the area of a rectangle is an essential skill that can be applied in a variety of real-world situations.

Additional Resources

For further reading on this topic, we recommend the following resources:

References

About the Author

The author of this article is a mathematics educator with over 10 years of experience teaching geometry and other math subjects. They have a passion for making complex math concepts accessible to students of all ages and skill levels.