Question

what is the area of the shaded region?
write your answer as a whole number or a decimal rounded to the nearest hundredth.
square centimeters

Explanation:

Step1: Calculate the area of the larger square

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. For the larger square with \(s = 39.8\) cm, \(A_{large}=39.8^2=39.8\times39.8 = 1584.04\) \(cm^2\).

Step2: Calculate the area of the smaller square

For the smaller square with \(s = 16.9\) cm, using the area formula \(A = s^2\), \(A_{small}=16.9^2=16.9\times16.9=285.61\) \(cm^2\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A\) is the difference between the area of the larger square and the area of the smaller square. So \(A=A_{large}-A_{small}\). Substitute the values: \(A = 1584.04−285.61=1298.43\) \(cm^2\).

Answer:

\(1298.43\) square centimeters