irregular shape measurements - Area calculations of odd shapes..

[RSbyTaschen]

How do you measure the area of an irregular shape where the only practical measurement to hand is the circumference? Sub dividing the shape into smaller right angle shapes is not appropriate or precise enough. Sorry :-(

[84-1093879891]

If you can get the circumference, you should be able to determine the radius. It then becomes a matter of calculating the area of a circle and then using a chord length or angle of rotation to determine the area of a particular sector.

It's a lot easier to explain if I had a layout plan.

[RSbyTaschen]

Thanks Tony for the reply:

Please follow my logic on this & see if it makes sense…

1. You measure the circumference of the shape and it comes to 18m.

2. Using this circumference you create a square consisting of 4 equal sides of 4.5 meters.

3. To find the area of the square you multiply two of the sides i.e. 4.5 x 4.5 = 20.25 sq m

4. Thefefore the area of the square is 20.25 meters. This must be the same area as the original shape..

Or am I being a Muppet..

[84-1093879891]

"It's time to play the music, it's time to light the lights, it's time to get things started...." ;)

You need more data than just the circumference. An 18m arc could be from a circle of radius 10m or a circle of 100m, which would yield wildly different areas (90m² and 900m², if you're intetested!) You need to determine a chord length and/or a sector angle, and or a radius. Are any of these possible?

[RSbyTaschen]

OK, OK, I’m am a Muppet!

My problems is that a have a bizarre shape to cover (with turf, as it happens) and I’m trying to get an accurate surface area estimate (plus-minus 5%)

For a bizarre shape, think of the state of Texas. If you’re straining, take a look here: http://fermi.jhuapl.edu/states/maps1/tx.gif

Short of numerically covering the area in rectangles adding them together to get a total, what are the alternatives?

I do not have a musical bone in my body and therefore your reference to chord length with relation to the calculations escapes me.

Anybody seen a pig in high heels??

Cheers.

Fozzi

[84-1093879891]

Using metre squares rounded-up will give you a reasonably accurate estimate of the area. I know several QSs still using that method!

For future reference, a chord, in reference to geometry, is a straight line joining any two points on the circuference of a circle, and a sector is an area of a circle bounded by two radial lines (lines running from the origin at the centre out to the circumference)...



...are you paying attention at the back of the class? ;)

[RSbyTaschen]

Thanks again Tony,

You have now got me interested in secondry school geometry again! Do you know any good sources of this stuff on the WWW? (aimed at Muppet's of course)

Cheers.

[84-1093879891]

I think the BBC have some pages aimed at schoolies doing O Levels (or whatever they're called this year). My younger daughter claims that she uses their site for 'revision', but every time I look over her shoulder, there seems to be a picture of Emineminem or 50 Pence glaring back at her.

http://www.bbc.co.uk/schools/sosteacher ... aths.shtml