How to Find the Area & Perimeter of a Square on a Coordinate Plane
Finding the area and perimeter of figures on a coordinate plane combines the properties of coordinate planes with the properties of geometric figures. After you understand the process of using the coordinate plane to find the perimeter and area of a square, you can use the same strategy to find the perimeter and area of many different shapes.
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Instructions
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1
Identify two corners of the square that make up one side.
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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
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Solve for distance using the formula:
√(4^2 + 7^2)
= √65
= 8.06
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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
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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
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Tips & Warnings
To find the perimeter and area of other shapes on a coordinate plane, identify the formulas for their areas and perimeters, then use the distance formula to identify the values for the sides you need.
