Help with an algorithm

[toxic drift]

I'm having trouble with an algorithm
let's say I have 3 rectangles, the sides of each rectangle are parallel to the x and y axis.
These rectangles can overlap, the goal is to find the area of all rectangles minus the intersection.

I have a few test cases and the area it's supposed to result in

Here's what I tried
I tried calculating the area of each of the 3 rectangles
Then I calculated the intersection between rectangles 1 and 3, 1 and 2 and 2 and 3, and substracted that.
I can't get that result.

Can someone help me out with a hint or what I'm doing wrong with my thought process

[elfin furnace]

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[toxic drift]

I'm not supposed to solve this by going through all the points in the region of the rectangles, as that would be inefficient

[next linden]

Then I calculated the intersection between rectangles 1 and 3, 1 and 2 and 2 and 3, and substracted that.
That's good but you forgot one crucial step.

You need to add the intersection of rectangle 1, 2 and 3 to that again

[toxic drift]

thank you

!solved