Question

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

Explanation:

Step1: Calculate area of outer square

The side length of the outer square is \( 37.8 \) mi. The area of a square is side length squared, so the area \( A_{outer} = 37.8^2 \).
\( 37.8^2 = 37.8\times37.8 = 1428.84 \) square miles.

Step2: Calculate area of inner square

The side length of the inner square is \( 26.8 \) mi. The area \( A_{inner} = 26.8^2 \).
\( 26.8^2 = 26.8\times26.8 = 718.24 \) square miles.

Step3: Calculate area of shaded region

The shaded area is the area of the outer square minus the area of the inner square, so \( A_{shaded} = A_{outer} - A_{inner} \).
\( A_{shaded} = 1428.84 - 718.24 = 710.6 \) square miles.

Answer:

\( 710.6 \)