# Help with a quick (hopefully) calculation.

#### MiniThug

##### Golden Member
Okay well maybe im just an idiot and am forgeting how to do this but someone help me out with this calculation. I have several just like it to do so after the first one is down it should serve as a good example to go by.

I am evaluating surface area and have a curved wall that I need to calculate. It is not a half circle, that would be too easy, yet an arc. I just need to find the lenght of the arc so I can take that and mult by the height and move on.

Heres what I know about the arc. Its base is 168" and it protrudes 40" from the base in the center of the arc.

Here is an image

Thanks

#### nafhan

##### Member
It's been a while since I've take calculus, but I'm pretty sure to find the area under a curve, you will have to get the formula for the curve and integrate above the x axis. I'm at work right now, so I don't really have the time and on top of that I'm not sure if you can find it, but to get the exact area you will need the formula for the curve. Hope that helps

#### Bulldozer

##### Senior member
Are you given any more information about the arc? You can't determine the length of the arc with just the vertical and horizontal lengths.

#### MiniThug

##### Golden Member
I wasnt sure if you could calculate the area or not.

I figured you could use the opposite and adjacent lengths to find the angle of the arc and then possibly find the arc length some how.

Guess not.
Thanks anyway guys, Ill just have to eyeball it.

#### eLiu

##### Diamond Member
Uhh...to find the length of the arc...if you flip it over, this arc would make a nice pretty elipse. I don't remember what the formula for an elipse is...but with the measures (convert them to xy coords) of the axes, you can reach what the eqn is. Once you have the eqn, use the distance formula to figure out how far a particle would travel to traverse the entire arc...and divide by 2. Then voila, length of arc =)

#### Dark4ng3l

##### Diamond Member
I think the formula for an ellipse is ((x-h)^2)/a^2 + ((y-k)^2)/b^2 =1

#### PowerEngineer

##### Diamond Member
Not exactly sure what's being asked, but I'll assume this curved wall is cylindrical (i.e. the curve is a section of a circle and the height is a fixed vertical length). Let's pick a center point for the circle; draw a radius "R" to each end of the 168" line connecting the two ends of the arc. The result is obviously an isoceles (spelling?) triangle. Now add another radius "R" bisecting the angle at the center point as well as the 168" line. Of course, the intersection forms right angles, and the length of this line from center to line is "R" minus the 40". This means that R*R = 84*84 + (R-40)*(R-40), so you should be able to determine R (I get 432.8, but I always make math mistakes). Knowing all three sides of the isoceles triangle, you can find the angle between the two "R" sides. That angle divided by 360 and then multiplied by 2*PI*R should give the length of the arc. Multiply by the height and you should be done.