Question

GEOMETRY Express the area of each figure as a monomial. a. 9a3b6b. 9a3b8c. 18a3b6d. 18a3b8

Answer 1

Given: A rectangle with the dimension below:

`\begin{gathered} \text{length}=6a^2b^4 \\ \text{width}=3ab^2 \end{gathered}`

To Determine: The area of the given rectangle:

The area of any given rectangle is calculated by the formula:

`A_{\text{RECTANGLE}}=\text{length}* width`

In other to calculate the area of the given rectangle, we would substitute for the length and width in the formula. Therefore, the area of the given rectangle is as calculated below:

`\begin{gathered} A_{\text{RECTANGLE}}=6a^2b^4*3ab^2 \\ A_{\text{RECTANGLE}}=(6*3)(a^2* a)(b^4* b^2) \\ A_{\text{RECTANGLE}}=18a^3b^6 \end{gathered}`

Hence, expressing the area of the figure given as a monomial gives us 18a³b⁶