6 Tips to calculate Area of composite Geometrical Figures
 Mar 29, 2016
 Sudipto Das
Mensuration is a common topic in mathematics. Students generally find it easy to find the area of known geometrical figures like circle, rectangle, square, triangle etc. from the figures provided in a problem. But what happens when they come across composite figures? They generally feel very uncomfortable with such problems. There are some tactics through which the problem can be solved. Let's go through some tips to calculate the area of complex geometrical figures with an example.

Careful Observation
Observe the figure closely. Don't feel intimidated by the complex nature of the figure. Keep faith in yourself that you can actually solve the problem.

Try to break down the figure into simple, known geometrical figures
Simple geometric figures like rectangle, triangle, semicircle, circle, square etc. are merged together to form a composite geometric figure. Try to break down the sample composite figure into simpler figures in your mind. These simple figures should be known to you. Channel your thinking pattern this way as soon as you encounter a problem connected with composite figures.

Sketch the outlines of Simple Figures in the sample Compound Figure
As soon as you figure out some imaginary simple figures in your mind for the complex problem, put your plan into action. Sketch the outlines of those specific simple figures in the problem. It's advisable to sketch those outlines in a manner which is slightly different from the sketch of the main sample problem for easy recognition. A sketch using dotted lines (or something similar) for the simple imaginary figures is perfectly suitable for this method. The example shown below can be referred for an easy explanation on this subject.

Make sure that Simpler Figures don't overlap each other
If areas of the sketched simpler figures overlap each other, you will not be able to get a correct solution of the problem. It will also cause confusion in the entire process which may get you to a wrong answer. Make sure that they don't overlap each other.

Calculate the Areas of the simpler known Figures separately
After the sketching part is over, it's time to calculate the areas of the individual simpler figures separately using the information available in the problem.
 Calculate the total of the areas of the simpler figures to get the correct result
The last step is simple addition of the areas of the simple figures that you found before. That will give you the final result which will be the area of the composite figure itself.
All these can be explained using a suitable relevant example like the one below:
Let's assume that the following diagram is your sample problem. The information required for solving this problem is provided in the figure itself. The diagram is not drawn to scale.
Image source bit.ly/1RrVAgX
The composite sample figure (shown above) is broken down into simpler figures by extending the line from the point O to D like this figure shown below. A yellow colored line is used for easy recognition.
Now you can easily detect the two figures from the above diagram. One is a semicircle and the other is a rectangle. If you can calculate the area of the semicircle and the rectangle in this compound figure and add them up, you'll be able to get the correct result. That result will be the area of the compound figure.
Solution
Values provided
AO=OD= 4cm (This is the radius, represented by 'r'),
CD=AB=6cm
Calculation of Area of the Semicircle
Area of the circle= π x (r^2) ['r' represents the radius of the circle]
Area of the semicircle = ½ x π x (r^2) cm^2
= ½ x π x (OD^2) cm^2
= ½ x π x (4^2) cm^2
= ½ x (22/7) x 16 cm^2
= 25.142 cm^2 (correct to 2 units after decimal)
Calculation of Area of the Rectangle
Length= AD=BC= (AO+OD)= (4+4)cm= 8 cm
Breadth=CD=AB= 6cm
Area of the rectangle = Length x Breadth
= (8 x 6) cm^2
= 48 cm^2.
Calculation of Area of the Composite Figure
Final Area= Area of the semicircle + Area of the rectangle
= (25.142 + 48) cm^2
= 73.142 cm^2
The area of the given composite figure is 73.142 cm^2.
If you want to get an example of a more difficult sum, then you can have a look at this problem designed in the shape of a heart.
So you can see that the problem is not that difficult. Just follow the 6 steps mentioned above and you'll master the entire procedure. Remember that practice makes a man perfect. So keep on practising these types of sums for a better performance in this subject. Good luck!
Sudipto Das
Sudipto writes technical and educational content periodically for wizert.com and backs it up with extensive research and relevant examples. He's an avid reader and a tech enthusiast at the same time with a little bit of “Arsenal Football Club” thrown in as well. He's got a B.Tech in Electronics and Instrumentation.
Follow him on twitter @SudiptoDas1993
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