Question

what is the area of this rectangle? the area of the rectangle is (use the operation symbols in the math palette as needed. simplify your answer.) $\frac{3}{2}b + 6$ ft $\frac{2}{3}b$ ft

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=\frac{3}{2}b + 6$ and $w=\frac{2}{3}b$.

Step2: Multiply length and width

$A=\frac{2}{3}b\times(\frac{3}{2}b + 6)$.
Using the distributive property $a(b + c)=ab+ac$, we have $A=\frac{2}{3}b\times\frac{3}{2}b+\frac{2}{3}b\times6$.

Step3: Simplify each term

For $\frac{2}{3}b\times\frac{3}{2}b$, $\frac{2}{3}\times\frac{3}{2}b^{2}=b^{2}$.
For $\frac{2}{3}b\times6$, $\frac{2\times6}{3}b = 4b$.
So $A=b^{2}+4b$.

Answer:

$b^{2}+4b$ square - feet