The Shaded Region Trick: When Subtraction Fails, Slice Through

Added: 2026-06-01

[00:00:00]How would you find the area of this blue shaded region? On many shaded region area questions, we might [music] think to find some total area and then subtract away regions like these two white triangles. The problem in this particular case is we don't know enough information about those two triangles.

[00:00:16]In fact, we can stretch and squish this figure and we can see that the white areas are variable.

[00:00:23]However, if we split the blue shaded region along [music] this diagonal, we create two different triangles and we can calculate the area of each one of these triangles with our triangle area formula A = 1/2 [music] BH, where the bases of each of these triangles are 3 and 6 and the height of these triangles are 8 and 5.

[00:00:43]Pluging those values into our formula gives us an area in the right triangle [music] of 12 and an area in the left triangle of 15. Adding those two areas together gives us a total of 27. [music] And no matter how we stretch and squish this figure, that area of 27 [music] is what remains.