Question

find the area of the following square. write your answer in simplest form. be sure to include the correct unit in your answer. $2\frac{3}{4}$ mm

Explanation:

Step1: Convert mixed number to improper fraction

The side length of the square is \(2\frac{3}{4}\) mm. Convert it to an improper fraction: \(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}\) mm.

Step2: Calculate the area of the square

The formula for the area of a square is \(A = s\times s\) (where \(s\) is the side length). So, \(A=\frac{11}{4}\times\frac{11}{4}\).
Multiply the numerators and denominators: \(\frac{11\times11}{4\times4}=\frac{121}{16}\).
Convert \(\frac{121}{16}\) back to a mixed number: \(\frac{121}{16}=7\frac{9}{16}\).
The unit for area of a square with side in mm is \(mm^{2}\).

Answer:

\(7\frac{9}{16}\) square millimeters (or \(7\frac{9}{16}\text{ mm}^2\))