For this question, Greg said that you have to say I don’t know because we don’t have enough information about what kind of quadrilateral it is. The answer makes sense to me but I often struggle with just assuming the shape based on how the figure looks like so in this case since it looks like a rectangle I assumed it to be rectangle and said it is true so I want to understand if the question would always specifically mention what figure it is and we don’t have to go by the shape?
Another question is, let’s say if it was a rectangle then would area really be half of it because it depends on wat we take the height as, for eg. if you refer to the picture below where I have marked the labels the height of the triangle could be KL which is equal to AC or MC so how can we definitely say that triangle’s area is half the rectangle if question mentions that ABCD is a rectangle because the two heights have completely different lengths so my hunch is even if we do take different heights bases also change so if height is KL then the base would be CD and if height is MC then the base would be KD so that way their areas can be equal with different heights
I want to understand if this deduction is correct?
You can’t assume angles without explicit statements about them (being 90 degrees, etc.) They will let you know if it is indeed a rectangle either explicitly or by marking 90 degree angles.
Now lets just assume that the questions explicitly says it is a rectangle to address your other question.
As for your second question, you can indeed try to solve the area of the triangle that way using CM as the base, but there would be no reference point for the base DK. The base would no longer be CD in that case. So, we pick a base and height that have clear reference points with the rectangle ABCD.
Basically, we choose base and height to match quantities that we can compare: CD and AC. Theres no use in picking quantities we dont have a reference too.
Heres a definition of area of triangles:
" We can choose any of the three sides of a triangle to call the base. The term “base” refers to both the side and its length (the measurement).The corresponding height is the length of a perpendicular segment from the base to the vertex opposite of it"
Just to be clear, yes, the changing of base and height will be proportionate such that the area will always be the same value. Here, we just only have info for 1 pair of Base and height
Right…so basically if CM is the height then base has to be KD because base would be the one were perpendicular’s end point is present and if KL is the height then CD would be the base right so can we definitely say if this was a rectangle then triangle’s area is half of rectangle?
