How To Calculate The Area Of Irregular Shapes

Our mind has a fling for perfect geometry and shapes. We seek alignment and a golden ratio in everything we do. However, our universe has come with different plans. There are a lot of areas where irregularities play a significant role. 

Haphazard shapes are not new to anyone. Now, it’s easy to calculate the area and dimensions of regular shapes like squares, rectangles and circles. But, what if you come across an object that has no clear edges or sides. This article will look at methods to calculate the area of irregular shapes with area of irregular shapes examples.

So, we know that regular shapes are the ones with definitive sides with specified lengths. On the other hand, irregular shapes are polygons with more than five sides. Polygons translate to many sides. 

Therefore, a shape with many sides with irregular lengths is called an irregular shape. To calculate the area of such shapes, we must derive regular shapes in them. This we can do by breaking down a given shape into several regular-shaped structures. 

So, you can break down an irregular shape into squares, triangles etc., and calculate their area by routine methods. 

Method of area calculation

We can use several methods to calculate the area of irregular shapes. Discussed below are the methods to reach a conclusive answer:

  • We can divide the given irregular polygon into various regular shapes and find out the cumulative area of each regular shape.
  • We can also evaluate the area of such shapes using unit squares.
  • If the irregular shape has curves, we can still divide it into regular shapes and calculate the area accordingly.

Area evaluation using unit squares

This is one of the common ways to find areas of irregular shapes with curves. The method is simple, but it does not apply to perfect circles or semicircles. Similarly, irregular quadrilaterals are also out of the purview of this process. In this method, you have to devise a chart with squares of equal dimensions. 

That is to say, the area of all the unit squares must be the same. Next, you superimpose the given irregular shape on this chart. Some parts of the given shape will occupy perfect squares, and some will only occupy a part of the square. 

So, if the number of perfect square occupancy is 4 and the number of part occupancy is 4 quarters, the total area will come out to be 6 square centimetres. 

Area evaluation of irregular shapes with square edges 

As discussed earlier, certain irregular shapes were out of the ambit of unit square evaluation. For this reason, we have arrived at a method where we divide the irregular shapes with curved edges into one or more regular shapes. 

Next, we calculate the area of each regular shape individually. The individual calculations have to be added up at last to reach the final answer. 

Area evaluation of irregular shapes with curved edges 

The area evaluation process of such shapes follows the same discourse as above. Hence, we divide the given irregular polygon into one or more regular shapes. So, if there is a round edge attached to the shape, we draw a diameter to conclude the resulting circle or semicircle. 

So, if you may get squares, rectangles, triangles, circles or semicircles in the end, calculate the area of such regular shapes individually, then add all these areas to reach your final answer. If you get a semicircle, the calculation method would be ½ πR², where R is the radius of the semicircle, which is half of the diameter. 

Similarly, if you get a triangle, in the end, you can calculate the area by using the method, ⅓ base X perpendicular. If the triangle is not right-angled, draw a perpendicular from the median of the base. 

Now, calculate the length of the perpendicular using the Pythagoras theorem. Lastly, the area calculation of squares and rectangles is fairly simple. For squares, if you have to square any given side and rectangle, you have to find out the product of length and breadth. In the end, sum up all the individual areas to arrive at your answer. 

Area evaluation using graph

Certain objects defy the laws of linear calculation. For such objects, we have to adopt certain complex approaches. 

  • One such object is a leaf. Now, the leaf does not follow the laws of polygons. Hence, we draw the leaf on the graph paper to find out the approximate area. 
  • Once you have figured out all the edges and mimicked the leaf on the graph paper, we move on to the next step. 
  • The next step involves counting of unit squares that the leaf occupies. Quite obviously, there will be some squares with complete occupancy and some with partial only. 
  • The catch here is that the square with more than half occupancy will also be counted as 1 unit square. 
  • So, you will start by counting all the whole squares. Next, you have to find the squares with more than half occupancy. 

Add these squares to your sum. Now, the squares with less than half occupancy will be taken as zero. So, the final answer would be the sum of unit area of all squares with full occupancy and the sum of unit area of all squares with more than half occupancy. 

Conclusion

We have discussed in detail all the methods to calculate the area of irregular shapes. Practice complex problems based on the principles above to refine your skills. 

This elementary mensuration has found its place in various competitive examinations. So, you must be careful when practising such questions. Additionally, memorise the formula for area calculation for different shapes.

Frequently Asked Questions 

  • What are irregular shapes? 

Irregular shapes are polygons with irregular lengths. These shapes do not have equal angles and equal sides.

  • How to calculate the area of irregular shapes?

To calculate the area of irregular shapes, we first divide them into regular shapes by drawing imaginary edges. Next, we add up the individual area of all such regular shapes to conclude. 

  • What are the applications of area evaluation methods of irregular shapes?

The methods discussed above have wide applications in the architecture industry. Additionally, industries like interior designing, map drawing and marking up agricultural fields also find applications of these methods.

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