Use the area formula A=s to the second power to find the area of square A (-7,6) B (-2,-6) C (10,-1) D (5,11)
To find the area of a square, we need to calculate the length of one side of the square. We can do this by finding the distance between any two consecutive points. Let's calculate the length of the side AB:
Using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
AB = √[(-2 - (-7))^2 + (-6 - 6)^2]
= √[(5)^2 + (-12)^2]
= √[25 + 144]
= √[169]
= 13
The length of side AB is 13 units.
Since all sides of a square are equal, the length of every side is also 13 units.
Now, we can calculate the area of the square by squaring the length of one side:
A = s^2
A = (13)^2
A = 169 square units
Therefore, the area of square ABCD is 169 square units.
To find the area of a square, you need to know the length of one side. However, the given points (A, B, C, and D) do not provide enough information to determine the side length of the square.
In order to find the area of the square, you'll need either the side length or another set of coordinates that can be used to calculate the side length.
To find the area of square ABCD using the formula A = s^2, where s is the length of one side of the square, we first need to calculate the length of the side.
To calculate the length of AB, we can use the distance formula, which is derived from the Pythagorean theorem. The distance between two points (x1, y1) and (x2, y2) is given by:
d = square root [(x2 - x1)^2 + (y2 - y1)^2]
Applying this formula to the points A (-7, 6) and B (-2, -6), we can calculate the length of AB:
dAB = square root [(-2 - (-7))^2 + (-6 - 6)^2]
= square root [5^2 + (-12)^2]
= square root [25 + 144]
= square root [169]
= 13
Since square ABCD is a square, all sides have the same length. Hence, the length of AB is also the length of BC, CD, and DA. Therefore, s = 13.
Now, we can use the formula A = s^2 to find the area:
A = 13^2
= 169 square units
So, the area of square ABCD is 169 square units.