Would the answer on mini question be a unknown number like "a"?

Module 2 Day 12 Your Turn Part 2 Mini Question
So why would the answer be an unknown number when we know the perimeter of the quadrilateral? Or maybe even if the info is not enough, would the answer be an unknown number if we set x in the question?

@victorioussheep Good question!
It's true that we know the perimeter of the quadrilateral, but the important thing is that the circle isn't fully inscribed in it. You can see that it only touches 3 sides, not all 4. That means you unfortunately can't use the formula from the video if you try connecting the center of the circle with all of the vertices, you'll see that the bottom triangle does not have area (1/2)(b)(r) (because r is not the height).
In general, it's definitely a good idea to check and make sure all the conditions for some result are satisfied before applying it, just to be safe
Let me know if you have any other questions!

Then would it be possible if we cut the side that hasn't touch the circle and make it touch the circle? (Like pushing the side or draw a new line that touches)And then we can solve the rectangle that has been cut?

@victorioussheep Yep, that would be possible, because the circle is then inscribed! By the rectangle that has been cut, do you mean the portion of the original quadrilateral that is everything except the "new quadrilateral" (that we can find the area of)? If so, it wouldn't necessarily be a rectangle, so it would unfortunately be a bit difficult to solve for the area of that (unless it's a "nice" shape and we know its sides)

Yeah, what I have meant by the cut rectangle is exactly the one you have said, so then would it be possible we solve it like that way?

@victorioussheep It would be possible if we had enough information! You would need the length of the constructed side, and also some information about that cut quadrilateral's side lengths (there are lots of ways to construct the fourth side, but I the easiest might be to draw it parallel to the quadrilateral's side that doesn't touch the circle, if that makes sense you'll get a trapezoid that is easier to find the area of than a random cyclic quadrilateral with no other special properties)

@audrey Thank you so much!

@victorioussheep No problem!

@audrey Thank you so much, Audrey!