Question

1. a summer camp is building a rectangular wooden sign to post at the entrance of the camp. the dimensions of the sign are shown below. write an expression for the area of the sign. 7c⁴d⁵ 3cd³

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the product of its length \( l \) and width \( w \), i.e., \( A = l \times w \).

Step2: Identify the length and width of the sign

From the diagram, the length of the rectangular sign is \( 7c^{4}d^{5} \) and the width is \( 3cd^{3} \).

Step3: Multiply the length and width

To find the area, we multiply these two expressions:
\[

$$\begin{align*} A&=(7c^{4}d^{5})\times(3cd^{3})\\ &=(7\times3)\times(c^{4}\times c)\times(d^{5}\times d^{3})\\ &= 21\times c^{4 + 1}\times d^{5+3}\\ &=21c^{5}d^{8} \end{align*}$$

\]

Answer:

The expression for the area of the sign is \( 21c^{5}d^{8} \).