Major triangle problem HELP

A

Ana.stasia

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The question is:
Calculate the surface area of a triangle that has two equal sides and a base side that is 12cm If the height which fits the base side in equal to a line which connects the middle of the base side and the middle of the other side.

I drew it.
Just in case of a language barrier ha is the height for the base side (side a).
120371753_354740662245898_8858926272244372352_n.jpg

However, I really have no idea what to do next. Please help.

Thank you.
 
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Ana.stasia said:
The question is:
Calculate the surface area of a triangle that has two equal sides and a base side that is 12cm If the height which fits the base side in equal to a line which connects the middle of the base side and the middle of the other side.

I drew it.
Just in case of a language barrier ha is the height for the base side (side a).
View attachment 21910

However, I really have no idea what to do next. Please help.

Thank you.
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Thank you. I managed to solve it. However, could you perhaps send me some information on how I can extract this formula on my own? I want to be able to get it from the triangle rather than memorize it.
 
Ana.stasia said:
I am stuck at the beginning. I don't know what to do. I was able to draw it but I am stuck at everything else.
Click to expand...
Use the following (AM is the median of the triangle)

The formula for the length of the median (AM)to side BC) = View attachment 21916
1601318640015.png
The formula for the length of the median to side BC = 1601318730180.png
 
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Ana.stasia said:
Thank you. I managed to solve it. However, could you perhaps send me some information on how I can extract this formula on my own? I want to be able to get it from the triangle rather than memorize it.
Click to expand...
What formula are you asking about? I don't see any mentioned. [EDIT: I see you asked this question after SK showed an unnecessary formula, though this question appears before it.]

The problem is a very special case. I would use the Pythagorean Theorem applied to triangle ANB, with the knowledge that your h_a = b/2, since triangles ACB and DNB are similar.
 
Dr.Peterson said:
What formula are you asking about? I don't see any mentioned. [EDIT: I see you asked this question after SK showed an unnecessary formula, though this question appears before it.]

The problem is a very special case. I would use the Pythagorean Theorem applied to triangle ANB, with the knowledge that your h_a = b/2, since triangles ACB and DNB are similar.
Click to expand...

Are the two triangles similar because their two sides are proportional, that is one has a, b and the other has a/2, b/2 and because they have the same angle?
 
Extending on response #5 (necessity is in the eye of the beholder):
1601373710365.png
MN = (1/2) * (2*NB2 + 2 * AN2 - AB2)1/2 = AN

2 * AN2 = 2*NB2- AB2 .....................................(1)

For triangle ANB - invoking Pythagorus

AB2 = AN2 + 36

Using above in (1)

2 * AN2 = 72- AN2 - 36

3 * AN2 = 36 ................................... We have height of the triangle (AN) and we know the base
 
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