Question

what is the area of the shaded rectangle? 2 1/2 in. 3/4 in. 1 5/8 in.² 1 14/16 in.² 15/16 in.² 2 3/8 in.²

Explanation:

Step1: Convert mixed - numbers to improper fractions

$2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$ and $\frac{3}{4}$ remains as is.

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 $w = \frac{3}{4}$. So $A=\frac{5}{2}\times\frac{3}{4}$.

Step3: Multiply the fractions

$\frac{5}{2}\times\frac{3}{4}=\frac{5\times3}{2\times4}=\frac{15}{8}=1\frac{7}{8}=\frac{1\times8 + 7}{8}=\frac{15}{8}$ square inches. There seems to be an error in the provided options as the correct answer $\frac{15}{8}=1\frac{7}{8}$ is not among them. If we assume there is a mis - typing and we recalculate with $l = 2\frac{1}{2}=\frac{5}{2}$ and $w=\frac{3}{4}$ correctly, the area $A=\frac{5}{2}\times\frac{3}{4}=\frac{15}{8}= 1\frac{7}{8}$. If we consider the closest option in terms of equivalent values after re - checking the problem setup, we may have some mis - understanding in the problem presentation. But if we calculate as per the standard rectangle area formula with the given side lengths, the area of the rectangle with length $2\frac{1}{2}$ inches and width $\frac{3}{4}$ inches is $\frac{15}{8}$ square inches.

Answer:

None of the given options are correct. The correct area is $\frac{15}{8}$ square inches.