Respuesta :

To answer this question you will Subtract the area of the large square and the area of the small square.

To find the side length of the small square, you will use the Pythagorean theorem.

If GD is 4 inches, than AG would also be 4 inches.

With in the work you will see the square root of eight being multiplied by itself, this eliminates the square root symbols.

Please see the attached picture for the work.
Ver imagen Mrscomputator

The edge of the small square and big square is √8 and 2√8. Then the area of the shaded region is 4 square inches.

What is a square?

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a square, opposite sides are parallel and all sides are equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

Let the side of a small square be a then the side of a big square be 2a.

The diagonal of the small square will be

[tex]\begin{aligned} a^2+a^2 &=4^2\\2a^2 &= 16\\a^2 &=8\\a &= \sqrt8 \end{aligned}[/tex]

Then the side of the big square will be √8.

The area of the shaded region will be

[tex]\rm Shaded \ area = area \ of \ big \ square - area \ of \ small \ square\\\\Shaded \ area = (2 \sqrt8)^2 - (\sqrt8)^2\\\\Shaded \ area = 32 - 8 \\\\Shaded \ area = 24[/tex]

More about the square link is given below.

https://brainly.com/question/13747846

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