Square $$ A B C D $$ has vertices $$ A(-2,-3), B(4,-1), C(2,5) $$, and $$ D(-4,3) $$. What is the area of the square? Select one: a. 28.25 units $$ ^{2} $$ b. 40 units $$ ^{2} $$ c. 400 units $$ ^{2} $$ d. 25.28 units $$ ^{2} $$

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Let the vertices of the square be $$ A(-2,-3) $$, $$ B(4,-1) $$, $$ C(2,5) $$, and $$ D(-4,3) $$.

1. The side length of the square can be calculated using the distance between two consecutive vertices. We start with $$ AB $$:

$$
AB = \sqrt{(4 - (-2))^2 + (-1 - (-3))^2} = \sqrt{(6)^2 + (2)^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10}
$$

2. Since all sides of a square are equal, the side length is $$ 2\sqrt{10} $$.

3. The area $$ A $$ of a square with side length $$ s $$ is given by:

$$
A = s^2 = \left(2\sqrt{10}\right)^2 = 4 \times 10 = 40
$$

Thus, the area of the square is $$ 40 $$ units$$^{2} $$.

The correct answer is option b.
The area of the square is 40 units².

Square has vertices , and . What is the area of the square?
Select one:
a. 28.25 units
b. 40 units
c. 400 units
d. 25.28 units

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Square has vertices , and . What is the area of the square? Select one: a. 28.25 units b. 40 units c. 400 units d. 25.28 units