Question

Чому дорівнює площа квадрата ABCD , якщо А(1,-1); С(3,5)

Answer 1

|AC| =√((3-1)²+(5+1)²)
|AC| =√40
S квадрата=(1/2)*AC*BD, AC=BD=√40
S=(1/2)*(√40)²
S=20

Answer 2

Calculating the Area of Square ABCD

To calculate the area of square ABCD, we can use the formula for the area of a square, which is given by the formula: S = a * a = a^2, where 'a' represents the length of one side of the square.

Given the coordinates of points A and C as A(1,-1) and C(3,5), we can calculate the length of one side of the square using the distance formula.

The distance formula is given by: d = √((x2 - x1)^2 + (y2 - y1)^2).

Using the distance formula, we can find the length of one side of the square, and then calculate the area of the square.

The length of one side of the square can be calculated as follows: d = √((3 - 1)^2 + (5 - (-1))^2) d = √(2^2 + 6^2) d = √(4 + 36) d = √40 d = 2√10

Now, we can calculate the area of the square using the length of one side: S = (2√10)^2 S = 4 * 10 S = 40

Therefore, the area of square ABCD is 40 square units.