Use the area formula A=s to the 2 power to find the area of square (-7,6) (-2,-6) (10,-1) (5,11)
To find the area of the square, we first need to find the length of one side of the square.
Let's find the distance between two of the given points. Using the distance formula, we have:
Distance between (-7, 6) and (-2, -6):
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-2 - (-7))² + (-6 - 6)²]
= √[5² + (-12)²]
= √[25 + 144]
= √[169]
= 13
Since the figure is a square, all sides are equal in length. Therefore, the length of one side of the square is 13.
Now, we can use the area formula A = s², where s is the length of one side of the square:
A = 13²
= 169
Therefore, the area of the given square with vertices (-7, 6), (-2, -6), (10, -1), and (5, 11) is 169 square units.
To find the area of a square, you need to know the length of one side. In this case, we are given the coordinates of four points that form a square: (-7, 6), (-2, -6), (10, -1), and (5, 11).
To determine the length of one side, we can use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's find the distance between points (-7, 6) and (-2, -6) as an example:
d1 = sqrt((-2 - (-7))^2 + (-6 - 6)^2)
= sqrt((5)^2 + (-12)^2)
= sqrt(25 + 144)
= sqrt(169)
= 13
Similarly, you can calculate the distances between the other pairs of points to find that all four sides have a length of 13.
Now that we know the length of one side, we can use the formula A = s^2 to calculate the area of the square:
A = 13^2
= 169
Therefore, the area of the given square is 169 square units.
To find the area of a square using the formula A = s^2, we need to determine the length of one side of the square.
To do this, we can calculate the distance between two adjacent vertices of the square, since all sides of a square are equal in length.
Let's calculate the distance between (-7, 6) and (-2, -6) to find the length of one side of the square:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(-2 - (-7))^2 + (-6 - 6)^2]
Distance = √[5^2 + (-12)^2]
Distance = √[25 + 144]
Distance = √169
Distance = 13
Therefore, the length of one side of the square is 13.
Now, we can use the formula A = s^2 to find the area:
Area = 13^2
Area = 169
Hence, the area of the square is 169 square units.