Question

find the area of the shaded rectangle. 2\frac{1}{2} in. 1\frac{1}{4} in. 2\frac{1}{8} in.^2 3\frac{2}{16} in.^2 6\frac{1}{4} in.^2 3\frac{3}{4} in.^2

Explanation:

Step1: Convert mixed - numbers to improper fractions

$2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$ and $1\frac{1}{4}=\frac{1\times4+1}{4}=\frac{5}{4}$

Step2: Use the area formula for a rectangle

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=\frac{5}{2}$ and $w = \frac{5}{4}$. So $A=\frac{5}{2}\times\frac{5}{4}$

Step3: Multiply the fractions

$\frac{5}{2}\times\frac{5}{4}=\frac{5\times5}{2\times4}=\frac{25}{8}$

Step4: Convert the improper fraction back to a mixed - number

$\frac{25}{8}=3\frac{1}{8}$ square inches

Answer:

$3\frac{1}{8}\text{ in.}^2$ (Note: There seems to be an error in the provided options as the correct answer is $3\frac{1}{8}\text{ in.}^2$ and it is not among them)