A Trapezoid Has An Area Of $200 \, \text{in}^2$. The Larger Base Is $14 \, \text{in}$ And The Height Is \$16 \, \text{in}$[/tex\]. Find The Smaller Base Of The Trapezoid.Select The Correct Response:A. $11 \,

Introduction

A trapezoid is a quadrilateral with at least one pair of parallel sides. In this article, we will delve into the world of trapezoids and explore the relationship between the area, height, and bases of a trapezoid. We will use the given information to find the smaller base of a trapezoid with an area of $200 , \text{in}^2$, a larger base of $14 , \text{in}$, and a height of $16 , \text{in}$.

The Formula for the Area of a Trapezoid

The area of a trapezoid can be calculated using the formula:

$$A = \frac{1}{2}h(b_1 + b_2)$$

where $A$ is the area, $h$ is the height, and $b_1$ and $b_2$ are the lengths of the two bases.

Given Information

We are given the following information:

• The area of the trapezoid is $200 , \text{in}^2$.
• The larger base is $14 , \text{in}$.
• The height is $16 , \text{in}$.

Finding the Smaller Base

We can use the formula for the area of a trapezoid to find the smaller base. Plugging in the given values, we get:

$$200 = \frac{1}{2}(16)(14 + b_2)$$

Simplifying the equation, we get:

$$200 = 8(14 + b_2)$$

Dividing both sides by 8, we get:

$$25 = 14 + b_2$$

Subtracting 14 from both sides, we get:

$$11 = b_2$$

Therefore, the smaller base of the trapezoid is $11 , \text{in}$.

Conclusion

In this article, we used the formula for the area of a trapezoid to find the smaller base of a trapezoid with an area of $200 , \text{in}^2$, a larger base of $14 , \text{in}$, and a height of $16 , \text{in}$. We simplified the equation and solved for the smaller base, which is $11 , \text{in}$. This problem demonstrates the importance of using formulas and equations to solve problems in mathematics.

Real-World Applications

Trapezoids have many real-world applications, including:

• Architecture: Trapezoids are used in the design of buildings, bridges, and other structures.
• Engineering: Trapezoids are used in the design of machines, mechanisms, and other devices.
• Geometry: Trapezoids are used to study the properties of shapes and their relationships.

Tips and Tricks

When working with trapezoids, remember to:

• Use the formula for the area: The formula for the area of a trapezoid is $A = \frac{1}{2}h(b_1 + b_2)$.
• Plug in the values: Make sure to plug in the given values into the formula.
• Simplify the equation: Simplify the equation to make it easier to solve.
• Check your work: Check your work to make sure you have the correct answer.

Common Mistakes

When working with trapezoids, be careful not to:

• Forget to plug in the values: Make sure to plug in the given values into the formula.
• Simplify the equation incorrectly: Simplify the equation carefully to avoid mistakes.
• Round the answer: Make sure to round the answer correctly to avoid mistakes.

Final Thoughts

Q&A: Trapezoids and Their Secrets

Q: What is a trapezoid?

A: A trapezoid is a quadrilateral with at least one pair of parallel sides.

Q: What is the formula for the area of a trapezoid?

A: The formula for the area of a trapezoid is:

$$A = \frac{1}{2}h(b_1 + b_2)$$

where $A$ is the area, $h$ is the height, and $b_1$ and $b_2$ are the lengths of the two bases.

Q: How do I find the smaller base of a trapezoid?

A: To find the smaller base of a trapezoid, you can use the formula for the area of a trapezoid and plug in the given values. Then, simplify the equation and solve for the smaller base.

Q: What if I forget to plug in the values?

A: If you forget to plug in the values, you will get an incorrect answer. Make sure to plug in the given values into the formula.

Q: How do I simplify the equation?

A: To simplify the equation, you can start by combining like terms and then dividing both sides by a common factor.

Q: What if I round the answer incorrectly?

A: If you round the answer incorrectly, you will get an incorrect answer. Make sure to round the answer correctly to avoid mistakes.

Q: What are some real-world applications of trapezoids?

A: Trapezoids have many real-world applications, including:

• Architecture: Trapezoids are used in the design of buildings, bridges, and other structures.
• Engineering: Trapezoids are used in the design of machines, mechanisms, and other devices.
• Geometry: Trapezoids are used to study the properties of shapes and their relationships.

Q: What are some common mistakes to avoid when working with trapezoids?

A: Some common mistakes to avoid when working with trapezoids include:

• Forgetting to plug in the values: Make sure to plug in the given values into the formula.
• Simplifying the equation incorrectly: Simplify the equation carefully to avoid mistakes.
• Rounding the answer incorrectly: Make sure to round the answer correctly to avoid mistakes.

Q: How can I practice working with trapezoids?

A: You can practice working with trapezoids by:

• Solving problems: Try solving problems that involve trapezoids.
• Using online resources: Use online resources, such as calculators and worksheets, to practice working with trapezoids.
• Working with a tutor: Work with a tutor who can help you practice working with trapezoids.

Q: What are some tips for working with trapezoids?

A: Some tips for working with trapezoids include:

• Use the formula for the area: The formula for the area of a trapezoid is $A = \frac{1}{2}h(b_1 + b_2)$.
• Plug in the values: Make sure to plug in the given values into the formula.
• Simplify the equation: Simplify the equation to make it easier to solve.
• Check your work: Check your work to make sure you have the correct answer.

Conclusion

In conclusion, working with trapezoids requires the use of the formula for the area of a trapezoid and careful simplification of the equation. By following the tips and avoiding common mistakes, you can find the correct answer and practice working with trapezoids.