Need help with my geometry

[RobertBrown]

 

[Egon]

[video]http://www.mathsisfun.com/area.html[/video]

 

[Lnk]

It's been so long since I got out of school, I can't remember how to solve this problem.
I can't even remember if its geometry, trigonometry or whatever. Maybe its early Alzheimer's?
Please help me find out how many square feet this is.

View attachment 465525

436.348 Sq Ft.

 

[smstonypoint]

436.3484845854290 square feet.

Steve

 

[ovrszd]

436.3484845854290 square feet.

Steve

Where ya been Steve????? We've been waiting for a solid answer!!!!!

 

[teejk]

Now somebody posted something above that jogged my memory. Put a triangle on both sides to form a rectangle. A) Calculate the area of that rectangle (even I remember that part). B)Then calculate the area of the triangles (a little fuzzy there but it is available quickly on-line). Subtract B) from A).

 

[dieselcrawler]

Due to the dimensions given, the length of the center rectangle was unknown. Sides A and C were known, so C Squared minus A squared equals B squared, in this case about 21.8 feet. Then it's easy...

 

[westcliffe01]

The main dimension that needs to be calculated is the width between the 10ft and the 30ft sides. One has to assume that the figure is symmetrical, else one needs at least 1 more dimension.. It is also assumed that the 10ft and 30ft sides are parallel.

Using Pythagoras, the distance is (24^2-10^2)^.5 = 21.817ft

Now you can slice off the triangle on the right and add it to the diagram on the left to make a rectangle. The rectangle is now 20ft x 21.817ft. That yields a surface area of 436.348 sq ft.

 

[Redneck in training]

Assuming the figure is symmetrical and the top and bottom lines are parallel. The height of the figure is calculated as (24^2 -10^2)^0.5 = (576-100)^0.5=21.81742'.
Then the area is 30*21.81742'=436.3485 as determined in several previous entries.

 

[LD1]

Yet another way to solve it. Now it is all Pathagorean.View attachment 465621

That is how I solved it. And get the 436.xxx as well.

But that is making the ASSUMPTION that the other diagonal leg is ALSO 24'. That wasnt a given as per the first drawing. As it stands, how the drawing is sketched up with current dimensions, and not knowing that it is symmetrical.....it is technically impossible to figure without some other numbers. Either angles, or length of the other diagonal.

Gathering more facts and knowing it is for a driveway apron.....I hope we can assume it will be symmetrical. Thus the conclusion of 436.xxx sq ft.

But its usually not good to automatically assume things in problems like this.

Exaggerated example, but solve this:

 

[LD1]

Cannot be solved. Need another piece of info. Either the overall height of the trapezoid, Distance between parallels.....that is assuming they are parallel (another assumption), One of the angles, etc.

Assuming they are parallel, simply adding an angle makes it solvable:


Sin60=h/24 will give us the height of the trapezoid. which would be 20.78.

then you can either use the trapezoid formula [(base + top) / 2 ] x height.......(10+30)/2 = 20.......20*20.78 = 415.xx

Or you can break it into right triangles. cos60=x/24 would give the third leg to the triangle on the right. Which would be 12.

So knowing the height, you now know everything needed.

 

[2LaneCruzer]

At first glance, it appears that one can't solve it without knowing the angle between the 30 foot and the 24 foot side. Besides, it isn't drawn to scale in the illustration, so measuring the angle would be nothing more than a guess.

Whoops! You beat me to it.

 

[GLyford]

Difference in grading the base will change the volume way more than the decimal points you all are calculating this to...

I ordered 3 yards for a project, the guy showed up with 4 on the truck, and I still ended throwing two bags in the mixer to finish it off.

So if the OP thinks he needs 8cy, I'd be really tempted to just order a whole truck, whether that turns out to be 9 or 10 yards. For whatever reason, when I'm forming up for slabs and walkways, they never seem to turn out too shallow, always a little too deep.

 

[SPYDERLK]

The source of the question made me trust the symmetrical appearance. If it had been from a test by a prof with history of messing with you, every answer would become an essay.

 

[tallyho8]

I am a member of several different forums. some with names that would seem to be much more logical to send a mathematical question to than a tractor forum. However, over the years, I have learned that TBN members have a vast amount of knowledge about any subject that you can comprehend, and I trust their answers more than those from any other forum I am a member of.

Hence, my reasoning for posting that question on this forum and my thanks to all who replied.

 

[LD1]

The source of the question made me trust the symmetrical appearance.

Agreed. But the source of the question wasnt revealed until post #13.

Prior to that, I would not have answered the question without more detail. After it was revealed that it was for a driveway apron, one can reasonably assume that it is symmetrical and the base parallel to the top. Thus the answer becomes easy. 436.xxx

So far, Dieselcrawler, 2lanecruzer, prichard, trailsend, vin-mil, RobertBrown, INK, Smstoneypoint, westcliffe01, Redneckintraining, and myself all have arrived at the correct answer.

RalphinVA got 520 the first go around, then 318
JPRambo got 480
Dap olksjj got 420
RSKY got 476
kidr got 615.1 (though I think he was joking)

So the real question is.....do you guys understand where you went wrong. We all learn from our (and others) mistakes. This thread is a nice learning exercise:thumbsup:

 

[k0ua]

Agreed. But the source of the question wasnt revealed until post #13.

Prior to that, I would not have answered the question without more detail. After it was revealed that it was for a driveway apron, one can reasonably assume that it is symmetrical and the base parallel to the top. Thus the answer becomes easy. 436.xxx

So far, Dieselcrawler, 2lanecruzer, prichard, trailsend, vin-mil, RobertBrown, INK, Smstoneypoint, westcliffe01, Redneckintraining, and myself all have arrived at the correct answer.

RalphinVA got 520 the first go around, then 318
JPRambo got 480
Dap olksjj got 420
RSKY got 476
kidr got 615.1 (though I think he was joking)

So the real question is.....do you guys understand where you went wrong. We all learn from our (and others) mistakes. This thread is a nice learning exercise:thumbsup:

I too solved the problem. (the nerd in me could not resist), but there was not point in posting after so many gave the correct answer. I used to really love to work these things. I know, that is sad isn't it?

 

[tallyho8]

Agreed. But the source of the question wasnt revealed until post #13.

Prior to that, I would not have answered the question without more detail. After it was revealed that it was for a driveway apron, one can reasonably assume that it is symmetrical and the base parallel to the top. Thus the answer becomes easy. 436.xxx

So far, Dieselcrawler, 2lanecruzer, prichard, trailsend, vin-mil, RobertBrown, INK, Smstoneypoint, westcliffe01, Redneckintraining, and myself all have arrived at the correct answer.

RalphinVA got 520 the first go around, then 318
JPRambo got 480
Dap olksjj got 420
RSKY got 476
kidr got 615.1 (though I think he was joking)

So the real question is.....do you guys understand where you went wrong. We all learn from our (and others) mistakes. This thread is a nice learning exercise:thumbsup:

LD1, I just posted a fairly easy question (that I didn't know the answer to) without complete details of angles, exact lengths, etc. because I just needed to know how much concrete to order and I always order at least 1/2 a yard extra so I didn't need an exact answer and I did not supply exact details because I did not think it would really matter. Most people would assume that the top and bottom lines were parallel from my original drawing and give me a close enough answer for my question, which they did.

Now you say you did not answer earlier because you did not want to assume that the lines were parallel until I revealed that it was for a driveway apron and then you "assumed" that they were parallel.

Well, so much for assuming. They actually are not parallel and the 2 sides are different lengths though I did not disclose this earlier because I did not want to over-complicate the matter and I had another part also that was a rectangle of 8' X 10' that I was easily able to figure was 80 sq. ft. that I added on to your correct answers without disclosing.

Now if any of you wish to tell me the exact measurement of my apron from the enclosed drawing, with more details, and the amount of concrete I should order, adding 1/2 yard extra, to be safe, please do so. I will see how much it varies from the 10 1/2 yards I am planning to order.

PS: The concrete is 6" thick.

 

[SPYDERLK]

Agreed. But the source of the question wasnt revealed until post #13.

Prior to that, I would not have answered the question without more detail. After it was revealed that it was for a driveway apron, one can reasonably assume that it is symmetrical and the base parallel to the top. Thus the answer becomes easy. 436.xxx

So far, Dieselcrawler, 2lanecruzer, prichard, trailsend, vin-mil, RobertBrown, INK, Smstoneypoint, westcliffe01, Redneckintraining, and myself all have arrived at the correct answer.

RalphinVA got 520 the first go around, then 318
JPRambo got 480
Dap olksjj got 420
RSKY got 476
kidr got 615.1 (though I think he was joking)

So the real question is.....do you guys understand where you went wrong. We all learn from our (and others) mistakes. This thread is a nice learning exercise:thumbsup:

I viewed tallyho8 as the source and suspected no trickery. I regarded the way to solve it as the most important to him. As in #19 u just have to sort the lines correctly.

 

[SPYDERLK]

Now if any of you wish to tell me the exact measurement of my apron from the enclosed drawing, with more details, and the amount of concrete I should order, adding 1/2 yard extra, to be safe, please do so. I will see how much it varies from the 10 1/2 yards I am planning to order.

PS: The concrete is 6" thick.

View attachment 465773

Are those angles at the top = ... and what value ?