what is the area of a regular quadrilateral (square) that has a radius of 10 square root of 2. The 10 square root of 2 is the x^2 (the hypotenuse) part of a 45-45-90.

What do you mean by the radius of a square? Are you referring to the inscribed circle or the circumscribed (outside) circle?

If 10 sqrt2 is the radius of a circumscribed circle, then the square inside the circle has side lengths of 20. The area is then 400.

it is only a square, no circle. the radius i am refering to is from the corner point to the midpoint of the square. and from the midpoint there is a line going straight down, thus forth a 45-45-90. it is like dividing a sqaure into 4 equal sections, each corner is in 1/4 of the square. then take one section, and cut that straight in half from the midpoint to the corner. that line is the 10 sqrt of 2.

In that case it is like the radius of a circumscribed circle, and the answer I gave is the correct one.

thank you

To find the area of a regular quadrilateral (square) with a given radius, we need to clarify a few things.

Firstly, a regular quadrilateral is not a square; it is a four-sided polygon with all sides and angles equal. A square is a specific type of regular quadrilateral with four equal sides and four right angles. If you are referring to a square, then we can proceed with the calculation.

Based on your description of the square having a radius of 10√2, it seems like you are referring to the length of the diagonal (hypotenuse) of one of its right triangles. In a square, the diagonals form right triangles with the sides of the square.

In a 45-45-90 right triangle, the ratio of the sides is 1:1:√2. If we let each side of the right triangle be x, then the hypotenuse, which is the diagonal of the square, will be x√2.

In this case, we have the hypotenuse (diagonal) as 10√2, so we can set up the following equation to find the side length, x:

x√2 = 10√2

To solve for x, we can divide both sides by √2:

x = 10

Therefore, the side length of the square is 10.

The area of a square is given by the formula A = s^2, where s is the length of the side. In this case, substituting the value of s, we get:

A = 10^2
A = 100

So, the area of the square is 100 square units.