A Rectangle Has A Length Of $6.5t$ Inches And A Width Of $12t$ Inches. What Is The Area Of The Rectangle Expressed As A Monomial?Enter Your Answer In The Box.[inches\[$^2\$\]]

**A Rectangle's Area: Understanding the Monomial Expression**

What is a Monomial?

A monomial is a mathematical expression consisting of only one term, which can be a number, a variable, or a product of numbers and variables. In the context of the given problem, a monomial expression represents the area of a rectangle in terms of a single variable, in this case, 't'.

Understanding the Problem

A rectangle has a length of $6.5t$ inches and a width of $12t$ inches. To find the area of the rectangle, we need to multiply the length by the width.

Calculating the Area

The area of a rectangle is given by the formula:

Area = Length × Width

Substituting the given values, we get:

Area = $6.5t$ × $12t$

To find the product of these two terms, we multiply the coefficients (6.5 and 12) and add the exponents of the variable 't'.

Multiplying the Coefficients

The product of the coefficients is:

6.5 × 12 = 78

Adding the Exponents

The exponent of 't' in the first term is 1, and the exponent of 't' in the second term is also 1. When we multiply two terms with the same variable and exponent, we add the exponents.

So, the exponent of 't' in the product is:

1 + 1 = 2

Writing the Monomial Expression

Now that we have the product of the coefficients and the sum of the exponents, we can write the monomial expression for the area of the rectangle:

Area = $78t^2$

Conclusion

In this article, we have seen how to find the area of a rectangle with a length of $6.5t$ inches and a width of $12t$ inches. We have also learned how to express the area as a monomial, which is a mathematical expression consisting of only one term.

Frequently Asked Questions

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

A: The formula for finding the area of a rectangle is:

Area = Length × Width

Q: How do I multiply two terms with the same variable and exponent?

A: When you multiply two terms with the same variable and exponent, you add the exponents.

Q: What is the difference between a monomial and a polynomial?

A: A monomial is a mathematical expression consisting of only one term, while a polynomial is a mathematical expression consisting of two or more terms.

Q: Can I have a rectangle with a length of $6.5t$ inches and a width of $12t$ inches?

A: Yes, you can have a rectangle with a length of $6.5t$ inches and a width of $12t$ inches. However, the area of this rectangle would be $78t^2$ square inches.

Q: How do I find the area of a rectangle with a length of $6.5$ inches and a width of $12$ inches?

A: To find the area of a rectangle with a length of $6.5$ inches and a width of $12$ inches, you would multiply the length by the width:

Area = $6.5$ × $12$ = $78$ square inches

Q: Can I have a rectangle with a length of $6.5t^2$ inches and a width of $12t$ inches?

A: Yes, you can have a rectangle with a length of $6.5t^2$ inches and a width of $12t$ inches. However, the area of this rectangle would be $(6.5t^2) × (12t) = 78t^3$ square inches.

Q: How do I find the area of a rectangle with a length of $6.5t^2$ inches and a width of $12t$ inches?

A: To find the area of a rectangle with a length of $6.5t^2$ inches and a width of $12t$ inches, you would multiply the length by the width:

Area = $(6.5t^2) × (12t) = 78t^3$ square inches