Coordinates are in grid units (1 unit = 1/40 of the SVG width). Angles always sum to 180 degrees.
The formulas behind the numbers
The area of a triangle is found with the shoelace formula, which works for any shape: multiply each x by the next y, subtract the next x times the current y, add the results around the figure, and halve the absolute total. This gives the same answer as the familiar base times height divided by two, but without needing to know which side is the base.
The perimeter is simply the sum of the three side lengths, each found from the distance formula, which is the square root of the sum of the squared differences in x and y. Each angle is found from the cosine rule: the cosine of the angle at a corner equals the sum of the squares of its two adjacent sides minus the square of the opposite side, all divided by twice the product of the adjacent sides.
Dragging a corner keeps all of this consistent. Angles always add to exactly 180 degrees inside a flat triangle. If you drag the three points into a straight line, the area collapses to zero, which is the tool telling you the shape is no longer a triangle.
Why use an interactive figure
Geometry is easier to understand when you can move it. Watch how the area changes differently from the perimeter: stretching one corner far out can add a lot of perimeter while adding little area. Watch an angle grow as you flatten the opposite side, and shrink as you raise it. These are the relationships that textbooks describe, made visible.
Frequently asked questions
Is this tool free? Yes, it is free and needs no login, and the drag interaction works on phones and tablets as well as desktop.
What are the units? Measurements are in grid units, where one unit is one fortieth of the drawing width, so you can compare shapes without committing to centimetres or inches.
Can the angles ever not sum to 180? Only if the points stop forming a triangle, for example when they line up. Otherwise they always sum to 180 degrees.