I know there’s math for this and it’s probably a relatively simple equation, but I’m trying to brute force it by calculating the area of each triangle assuming it’s a 3*6 grid.
It’s a slog.
Edit: Also I got stuck. The white part of the flag is the sum of a triangle roughly 1•6.32•6.7, and one roughly 5•2•6.7, but I forgot how to calculate the areas of scalene triangles. I know you have to make two right triangles out of them next, but I don’t know how to do that without just guessing and checking against the Pythagorean theorem, which is way more math than I want to do without a pencil and paper
Well, you can calculate the areas of blue triangles easily since they’re right triangles, than just calculate pink+blue area and substract the blue area that you calculated previously, repeat for white+pink+blue.
Yes, the area of a triangle is base times height over 2. The base is a side of your choice and the height is measured in a right angle to it (You may have to extend it in a straight line).
Lets split the flag into two triangles from corner to corner and consider the bottom right one (the other works the same way).
Chose the edge on the right flag edge as the base and the height of the triangle becomes the width of the flag.
All the colored triangles have the same height and by the look of it roughly the same base length.
I know there’s math for this and it’s probably a relatively simple equation, but I’m trying to brute force it by calculating the area of each triangle assuming it’s a 3*6 grid.
It’s a slog.
Edit: Also I got stuck. The white part of the flag is the sum of a triangle roughly 1•6.32•6.7, and one roughly 5•2•6.7, but I forgot how to calculate the areas of scalene triangles. I know you have to make two right triangles out of them next, but I don’t know how to do that without just guessing and checking against the Pythagorean theorem, which is way more math than I want to do without a pencil and paper
Well, you can calculate the areas of blue triangles easily since they’re right triangles, than just calculate pink+blue area and substract the blue area that you calculated previously, repeat for white+pink+blue.
Yep
Yup, I shouldn’t have started with white, lol
Blue: (.5(2•3))+(.5(1•6))=6
Pink: ((.5(4•3))*(.5(2•6)))-6=6
White (simplified): (3•6)-12=6
Yes, the area of a triangle is base times height over 2. The base is a side of your choice and the height is measured in a right angle to it (You may have to extend it in a straight line).
Lets split the flag into two triangles from corner to corner and consider the bottom right one (the other works the same way).
Chose the edge on the right flag edge as the base and the height of the triangle becomes the width of the flag.
All the colored triangles have the same height and by the look of it roughly the same base length.
Therefore the areas are equals.
I salute your work, we worked it out below :)