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sharath4
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Calculation of Area of Irregular Shapes

10/24/2011 4:09 AM

How to calculate the area of the following slot?

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Anonymous Hero
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#1

Re: Calculation of area of irregular shapes

10/24/2011 7:36 AM

The easiest way is to draw it in a CAD program and let the software calculate it.

However, traditionally I would break the shape into meaningful parts (i.e., circles and rectangles and triangles) and sum the parts' areas.

In some cases you may need to do some subtractions in the process or break things into triangles.

For instance, the arcs at the top is slightly more than 180° and the bottom is less than 180°, which leaves an irregular set of shapes at the top and bottom of the center. Here symmetry can be employed and the center section split into two trapezoids, which the ends can be broken off into triangles.

A simple High School trigonometry book will give you the formulas for areas of various shapes and how to calculate lengths based on angles (trigonometric tables).
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Mikerho
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#2

Re: Calculation of Area of Irregular Shapes

10/24/2011 9:07 AM

Here's what I do sometimes:

  1. Cut a piece of paper, that is larger than the area that you want to measure, to known dimensions.
  2. Weigh the paper.
  3. Then outline or trace the area.
  4. Cut the area out and weigh it.
  5. Weight of cutout divided by the weight of the whole piece of paper is equal to the percentage of the area of the original piece of paper.
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Anonymous Hero
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#3
In reply to #2

Re: Calculation of Area of Irregular Shapes

10/24/2011 9:21 AM

Clever.
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Mikerho
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#5
In reply to #3

Re: Calculation of Area of Irregular Shapes

10/24/2011 10:43 AM

Before they had electronic integration methods, this is how they obtained relative amounts of peaks on chromatograms.

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Anonymous Poster #1
#11
In reply to #2

Re: Calculation of Area of Irregular Shapes

10/28/2011 12:57 AM

could this be done with photogaphy?
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Mikerho
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#12
In reply to #11

Re: Calculation of Area of Irregular Shapes

10/28/2011 2:06 AM

As long as your paper has a sufficient uniformity of weight per area, yes.

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Anonymous Hero
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#14
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Re: Calculation of Area of Irregular Shapes

10/28/2011 7:13 AM

Be aware that a camera will distort the image through the lens.
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Anonymous Hero
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#4

Re: Calculation of Area of Irregular Shapes

10/24/2011 10:10 AM

Here is how I would do this problem. From your illustration I can't be sure, but it looks something like this:

I simplified the drawing to at least show you the mechanics of breaking this problem down into manageable steps.

The two semicircles are easy to calculate. The 10° is just my example, but we know the fractions (190°/360° and 170°/360°) of a full circle and the area of a circle is an easy formula. So, the calculations are simply the area of a full circle times the fraction of the circle.

The two trapezoids are next. Both are symmetrical, so we only need to calculate one and multiply by two.

I rotated the beige trapezoid left by 85° to make the calculation visually easier. I then subdivided the trapezoid with the dashed line to make a triangle and a rectangle.

Calculating the rectangle is easy if we find the length. To do that we go back to the triangle. We know that the hypotenuse is h^2 = a^2 + b^2 if the triangle is a right triangle.

I rearranged that formula to solve for d0 (d is the hypotenuse).

The total area is therefore the sum of all areas after you multiply the area of that trapezoid (A3 and A4) by two.

Since I can't see your illustration well, that tail is something you will have to figure out based on the tools I presented here.

Nevertheless, what I have shown you here is just one way to skin the cat, but you get the idea.
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TonyS
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#6
In reply to #4

Re: Calculation of Area of Irregular Shapes

10/24/2011 10:52 AM

You've got getter eyesight than me I couldn't see the dimensions even after taking the drawing in to Photoshop. One thing I did notice was there's no length given for the "tail" so don't knock yourself out over it.

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Anonymous Hero
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#7
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Re: Calculation of Area of Irregular Shapes

10/24/2011 12:08 PM

I am more interested in teaching the principles for problem solving. These principles apply in so many ways.
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sharath4
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#9
In reply to #4

Re: Calculation of Area of Irregular Shapes

10/25/2011 3:08 AM

Thank you very much Mr. Anonymous Hero

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phoenix911
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#10
In reply to #4

Re: Calculation of Area of Irregular Shapes

10/25/2011 7:56 AM

wow, how did you read that?

ga

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Mikerho
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#13
In reply to #4

Re: Calculation of Area of Irregular Shapes

10/28/2011 2:09 AM

Sorry I haven't been back until now, but GA for the in-depth analysis. Very good.

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phoenix911
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#8

Re: Calculation of Area of Irregular Shapes

10/24/2011 12:26 PM

Break it down into its components.

Then reach for your Mechinery's handbook.

Yes, CAD is much more quicker.

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Nando37
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#15

Re: Calculation of Area of Irregular Shapes

10/30/2011 12:46 AM

The dimensions are not readable
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