Advanced Area of a Triangle

philthy

New member
Joined
Mar 3, 2015
Messages
7
Hello all, first time poster!

I need a little help with the area of a triangle; however this is not that simple. I will be given a width and length of the triangle and I will need to calculate the area of a triangle exactly 1 inch bigger all around than the dimension entered. I cannot simply add 2 inches to each number I entered as it will not be correct because the corners of the triangle will be bigger than 1 inch. The angles will always be changing so I am looking for other ways to do this. Any ides? I need to make an excel spreadsheet where I type in the two numbers and the formula does all the work.

Please see the attachment for better clarification.

Thank you all in advance for your help!

Phil

P.S. I will have to do a similar thing to a trapezoid, but I think once this is figured out I can apply the same principle to it.
 

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Unclear.
Take triangle with sides 3-4-5: what will be given?

Your diagrams are also confusing:
seems to indicate outside dimensions given,
then a triangle 1 inch SMALLER inside...


Sorry if it is confusing. Let me try again...

What is happening is there will be a triangular hole cut into metal and I need a cover plate that is a triangular piece of metal that is offset exactly 1" bigger on the three sides. Using the information of the triangular hole, I will need to find the area of the bigger triangle. Still sounds confusing to me-I hope it is not.

I will only be given 2 numbers. One of the numbers will be the base (b) and one will be the height (h). (See new attachment). Figuring out the area of this triangle is easy. My dilemma is that using these numbers, I need to figure out the area of a triangle for the cover plate.

On the original attachment this is what I was trying to show:

Example 1: I will be given b=6 and h=6 (which is the triangles shown on the left). The triangles on the right are basically the numbers I am trying to get, but I had to draw it out on the computer to get the numbers. So a triangular hole with a b=6 & h=6 will require a triangular cover that has a b=14-9/16 & h=8-9/16. Is it possible to have a formula to figure this out for me without having to draw it?

Example 2: I will be given b=10 and h=6. See example 1, same principle.

Using excel, I will be inputting the b and h numbers into cells and have it calculate the area of the cover plate for me. There will be hundreds of different combinations of numbers to input for b an h so excel would work great to do this - if I knew a formula to do this for me.

I hope this is easier to understand. Thanks for the reply.

Phil
 

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Hello all, first time poster!

I need a little help with the area of a triangle; however this is not that simple. I will be given a width and length of the triangle and I will need to calculate the area of a triangle exactly 1 inch bigger all around than the dimension entered. I cannot simply add 2 inches to each number I entered as it will not be correct because the corners of the triangle will be bigger than 1 inch. The angles will always be changing so I am looking for other ways to do this. Any ides? I need to make an excel spreadsheet where I type in the two numbers and the formula does all the work.

Please see the attachment for better clarification.

Thank you all in advance for your help!

Phil

P.S. I will have to do a similar thing to a trapezoid, but I think once this is figured out I can apply the same principle to it.

I do not see anyway of doing this - unless you give some other constraint (like isosceles triangle or any of the other angles or another side). A general triangle can be defined with three parameters e.g. A-S-A or S-S-S etc.

You can do it graphically - because you assume the shape of the triangle.

Thus - I suspect you need another variable defined for unique answer.
 
You sure, Subhotosh?
If base and height are given, then it does not matter
where the height line meets the base line: same area.

AND, to simplify matters, may as well make it a right
triangle, base and height being the legs.

I'm gonna try a case both ways to see...

So take a 3-4-5 triangle - area = 6

Then increase each side by 1" → 4-5-6 - see the problem - it is not right-angled anymore.

I am not sure what does the OP really means.
 
I'll be using a = base and b = height

GIVENS:
a = ?
b = ?

c = SQRT(a^2 + b^2)

u = ASIN(a/c)
w = 90 - u/2
d = SIN(w) / SIN(u/2)

v = 90 - u
x = 90 - v/2
e = SIN(x) / SIN(v/2)

AREA = (a + e + 1) * (b + d + 1) / 2

If a=6 and b=6, above will return AREA = 44.3137....

If a=10 and b=6, above will return AREA = 64.0384....
Another:
If a=13 and b=17 : AREA = 167.8784....

How you input above into Excel is your problem; I never used it.

EDIT:
Above only applies to cases where the base and height
are legs of a right triangle.
Using 16 for height and 12 for base:
right triangle: 150 (new area)
height line at 1 : 149.31 (height line touches base 1 from either ends)
at 2: 148.74
at 3: 148.30
at 4: 147.98
at 5: 147.79
at 6: 147.73

Right triangle always gives maximum, of course.


Wow, I am impressed! This seems like the type of formula that I am looking for. These will always have the base and height as legs of a right triangle.

I will put this into excel and then draw a few out and compare the results, but from first glance it looks good. I will let you know what I find out. Thank you for spending some time helping me out.
 
I'll be using a = base and b = height

GIVENS:
a = ?
b = ?

c = SQRT(a^2 + b^2)

u = ASIN(a/c)
w = 90 - u/2
d = SIN(w) / SIN(u/2)

v = 90 - u
x = 90 - v/2
e = SIN(x) / SIN(v/2)

AREA = (a + e + 1) * (b + d + 1) / 2

If a=6 and b=6, above will return AREA = 44.3137....

If a=10 and b=6, above will return AREA = 64.0384....
Another:
If a=13 and b=17 : AREA = 167.8784....

How you input above into Excel is your problem; I never used it.

EDIT:
Above only applies to cases where the base and height
are legs of a right triangle.
Using 16 for height and 12 for base:
right triangle: 150 (new area)
height line at 1 : 149.31 (height line touches base 1 from either ends)
at 2: 148.74
at 3: 148.30
at 4: 147.98
at 5: 147.79
at 6: 147.73

Right triangle always gives maximum, of course.


I inputted this information into excel and it is close, but something is a little bit off and I can't figure out where yet. Can you please explain a little more about what some of the values are? I know some, but I am not going to pretend that I know them all. I have attached a picture showing the results that I got using excel, your area, and what I got when I drew it out on the computer. All in the same ballpark, but slightly off. I did this for all three examples and I attached my computer sketches as well. Thanks again for your help.
 

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  • Scan10002.jpg
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Hello all, first time poster!

I need a little help with the area of a triangle; however this is not that simple. I will be given a width and length of the triangle and I will need to calculate the area of a triangle exactly 1 inch bigger all around than the dimension entered. I cannot simply add 2 inches to each number I entered as it will not be correct because the corners of the triangle will be bigger than 1 inch. The angles will always be changing so I am looking for other ways to do this. Any ides? I need to make an excel spreadsheet where I type in the two numbers and the formula does all the work.

Please see the attachment for better clarification.

Thank you all in advance for your help!

Phil

P.S. I will have to do a similar thing to a trapezoid, but I think once this is figured out I can apply the same principle to it.
What is the shape of your triangle? Is it an isosceles, equilateral, ???
 
This may(?) help some "seeing" d and e, and the angles:
Code:
D

            [DG = DH = d
     H

G   A       [GA = AH = 1]




                           [AB = HK = c]

b   b



 
                         K
                             [BK = BL = 1]
I   C        a         B


F   J        a         L        E [EK = EL = e]
[IC=CJ=JF=FI=1]
Triangle ABC inside triangle DEF.
BC = a, AC = b, AB = c
FE = 1+a+e, FD = 1+b+d, DE = d+c+e

angleCAB = angleFDE = u
angleABC = angleDEF = v

angleDAG = w, angleADG = u/2 ; triangleADG = triangleADH
angleEBL =x, angleBEL = v/2 ; triangleBEK = triangleBEL


Thank you, I was able to get excel to give me the correct output now. BUT...and I allow you to beat me up for this.... I did misinformed you on one thing.... :oops:

This will be an isosceles triangle not a right right triangle. When I originally answered your question I was in the mindset that I basically had two right triangles and I guess "right triangle" was on my mind. I truly apologize for that mistake as I realize it is critical. Is it difficult to alter what you did to accommodate an isosceles triangle? I cant simply treat it as two right triangles and divide "a" by 2 and then double the answer at the end because I will have an overlap of the border. Thank you so much for the time you have spent helping me!
 
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