Area of Composite Figure

[The Tan Gent]

I need suggestions on how to find the area of the composite figure shown. I understand the concept of how to go about this, I am just stuck on determining some of the measurements from the diagram. My approach was to calculate the area of the rectangle and subtract the two right triangle areas, but I am stuck on finding some required measurements.

 

[Dr.Peterson]

I don't think there's enough information. You appear to be given the lengths of parts of the horizontal dimension, but not the whole, from which the other parts could be found.

Are you sure there isn't any additional information? For example, if we knew that the two hypotenuses are equal, we could work it out.

Problems like this should really be stated in words, to clarify its meaning. Are there words?

 

[The Tan Gent]

There were no words, except the directions simply stated to "Find the area of the composite figures. Round answers to the nearest whole number if necessary."

I was thinking that if the two hypotenuses were congruent, it could be solved. Maybe for my students, I will make that the case. I wanted to ask about this problem because I thought there was something I wasn't thinking of. I tried saying the top right segment was X and the missing leg of the leftmost right triangle was Y, which gave the equation Y=X+2 and I tried to think of another equation to use to solve a system. I thought I was going crazy that I couldn't figure out a high school area problem!

Thanks for verifying I'm not crazy (at least not THAT kind of crazy).

 

[Dr.Peterson]

Unfortunately, assuming the hypotenuses are equal doesn't lead to nice numbers, as I would have hoped; but then, rounding is expected.

I presume you copied the picture exactly, and there is no answer in the back of the book?

One thing you can do to make it obvious that there is missing information is to redraw the figure with a significantly greater width, keeping all labeled lengths the same, and see that there is nothing to prevent doing so (until it gets very wide!).

 

[Denis]

If the length of the rectangle is 10 + x (looking at top), then solution is:
7(x + 10) - 10*4/2 - 7(x + 2) = 3.5x + 43.

Sooooo....not quite enough information given.