I solved both of them using Algebra, which I don’t think I learned until I was 14.
This concept told me what it was because I’ve seen similar problems before.
Username checks out.
You don’t need algebra though. You can just use the common sense methods described in this thread.
Gah! I thought the question was to solve the AREA, not the perimeter. The perimeter was obvious to me. I don’t think you could solve for the area though.
No, you can’t solve the area with the information given.
Glad I’m not the only one
That was my problem too. I was just about to point out a fatal flaw in treis’ solution because it made an assumption that you can’t make (if one were trying to find the area). Finding the perimeter, however, I could see 5th graders working on this, especially if it was a bonus question, or at least one that was known to be harder.
This almost segues transverse lines (go with me on this). I remember struggling with those in grade school. Trying to remember which angles were the same, which ones were opposite and so on. Then one day I realized that you could take the two parallel lines and slide them together (in your head, anyways) and the acted like a single angle, at least WRT which angles were the same, opposite etc.
That goes with what Little Nemo was saying about being able to slide the edge in and out, if you can problem solve that in your head, that’s kind of what math is about.
Having said that, IMO, that’s not really what you want to do here. I’m guessing the point of this exercise was to learn that two unknown vertical parts add up to 12 and the two unknown horizontal parts add up to 10. What you can do with that knowledge is limited, but you can find the perimeter with it.
I solved the first one in my mind by sliding the right hand vertical line out so as to make a rectangle, and then realizing that this created a gap at the top that was the same length as the horizontal width of the small extension.
I solved the second one similarly by realizing that it was the same as a 9 by 11 rectangle except that the two 2cm horizontals added 4cm to the length.
Tricky problem. Took me a minute to puzzle it out. But then it became obvious.
being rectilinear is one clue. Realizing that breaking a line segment into multiple line segments doesn’t change their total length is the second clue.
I did the same. A good case of RTFQ.
At first glance the area thing through me off, but I just recently did some things that reminded how little area and perimeter are related in geometric shapes.