A Parallelogram Has A Base Length Of 18.25 M And A Height Of 7.4 M. Find The Area Of The Parallelogram.A. 25.65 M 2 25.65 \, M^2 25.65 M 2 B. 54.76 M 2 54.76 \, M^2 54.76 M 2 C. 135.05 M 2 135.05 \, M^2 135.05 M 2 D. 0.67 M 2 0.67 \, M^2 0.67 M 2

Introduction

A parallelogram is a type of quadrilateral with opposite sides that are parallel to each other. In this article, we will focus on finding the area of a parallelogram given its base length and height. The area of a parallelogram is a fundamental concept in geometry and is used in various real-world applications, such as architecture, engineering, and design.

What is the Area of a Parallelogram?

The area of a parallelogram is defined as the product of its base length and height. Mathematically, it can be represented as:

Area = base × height

Calculating the Area of a Parallelogram

To find the area of a parallelogram, we need to multiply its base length by its height. Let's use the given values of base length (18.25 m) and height (7.4 m) to calculate the area.

Step 1: Identify the Given Values

• Base length (b) = 18.25 m
• Height (h) = 7.4 m

Step 2: Calculate the Area

Using the formula Area = base × height, we can calculate the area of the parallelogram as follows:

Area = 18.25 m × 7.4 m = 134.85 m²

Rounding the Answer

Since the answer choices are given in two decimal places, we can round our calculated answer to two decimal places:

Area ≈ 134.85 m² ≈ 135.05 m²

Conclusion

In this article, we have learned how to calculate the area of a parallelogram given its base length and height. We have used the formula Area = base × height and applied it to a given example. The calculated answer is approximately 135.05 m².

Answer

The correct answer is C. $135.05 \, m^2$.

Additional Tips and Variations

• If the base length and height are given in different units (e.g., meters and centimeters), we need to convert them to the same unit before calculating the area.
• If the base length and height are given as fractions or decimals, we can use a calculator or perform the necessary arithmetic operations to calculate the area.
• The area of a parallelogram can also be calculated using the formula Area = base × height × sin(θ), where θ is the angle between the base and the height. However, this formula is not as commonly used as the basic formula Area = base × height.

Real-World Applications

The area of a parallelogram has numerous real-world applications, such as:

• Calculating the area of a building or a room
• Determining the amount of material needed for a construction project
• Finding the area of a piece of land or a plot of property
• Calculating the area of a garden or a park

Conclusion

Frequently Asked Questions

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

A: The formula for calculating the area of a parallelogram is Area = base × height.

Q: What if the base length and height are given in different units?

A: If the base length and height are given in different units, we need to convert them to the same unit before calculating the area.

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

A: Yes, you can use a calculator to calculate the area of a parallelogram. Simply enter the base length and height into the calculator and multiply them together.

Q: What if the base length and height are given as fractions or decimals?

A: If the base length and height are given as fractions or decimals, you can use a calculator or perform the necessary arithmetic operations to calculate the area.

Q: Can I use the formula Area = base × height × sin(θ) to calculate the area of a parallelogram?

A: Yes, you can use the formula Area = base × height × sin(θ) to calculate the area of a parallelogram. However, this formula is not as commonly used as the basic formula Area = base × height.

Q: What are some real-world applications of the area of a parallelogram?

A: Some real-world applications of the area of a parallelogram include:

• Calculating the area of a building or a room
• Determining the amount of material needed for a construction project
• Finding the area of a piece of land or a plot of property
• Calculating the area of a garden or a park

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

A: Yes, you can use the area of a parallelogram to calculate the area of a rectangle. Since a rectangle is a type of parallelogram, the formula Area = base × height can be used to calculate the area of a rectangle.

Q: What if I have a parallelogram with a base length of 10 cm and a height of 5 cm? How do I calculate the area?

A: To calculate the area of a parallelogram with a base length of 10 cm and a height of 5 cm, you can use the formula Area = base × height. Plugging in the values, you get:

Area = 10 cm × 5 cm = 50 cm²

Q: Can I use the area of a parallelogram to calculate the area of a triangle?

A: No, you cannot use the area of a parallelogram to calculate the area of a triangle. The formula for the area of a triangle is different from the formula for the area of a parallelogram.

Q: What if I have a parallelogram with a base length of 20 m and a height of 10 m? How do I calculate the area?

A: To calculate the area of a parallelogram with a base length of 20 m and a height of 10 m, you can use the formula Area = base × height. Plugging in the values, you get:

Area = 20 m × 10 m = 200 m²

Conclusion

In conclusion, the area of a parallelogram is a fundamental concept in geometry that has numerous real-world applications. By understanding how to calculate the area of a parallelogram, you can apply this knowledge to various fields, such as architecture, engineering, and design.