How to Find the Area & Perimeter of a Square on a Coordinate Plane
- 1). Identify two corners of the square that make up one side.
- 2). Substitute the coordinates into the distance formula. The distance formula is √(((x2 - x1)^2) + ((y2 - y1)^2)) = distance. It doesn't matter which of the "x" values you use for x1 or x2, as long as you keep the same order for the "y" values.
For example, if you discovered the coordinates of the two points were (2, 3) and (6, 10), the distance formula would look like this:
√(((6 - 2)^2) + ((10 - 3)^2)) = distance - 3). Solve for distance using the formula:
√(4^2 + 7^2)
= √65
= 8.06 - 4). Find the perimeter of the square using the distance that you calculated and the perimeter formula for a square. All the sides of a square are equal, so the perimeter, or distance around the figure, equals four times the distance of one side, or "4s."
Perimeter (P) = 4 x 8.06
P = 32.24 - 5). Find the area of the square by using the distance of the one side, and the formula for the area of a square. Area (A) = L x W. Since all sides of a square are the same, you can simplify the area of a square as: A = S^2.
A = 8.06^2
A = 64.96