Question

Find the area of the shaded region given in the figure.

Answer 1

Hey friend , Harish here.

Here is your answer.

This is really a interesting and tricky problem. So we have many hard solutions and a very simple solution for this problem.

Let's look for the simplest solution possible from our basics.

So for making it simple we need some we need to recall some basic concepts.

Recalling the basics :

1) $\mathrm{Area\ of\ \Delta} \mathrm{= \frac{1}{2}\times base\times height}$

So for same base and height areas of two triangles are equal.

Now lets see how to make it use this concept. A little construction will help here.

Construction :

Connect the point inside the quadrilateral to all the vertex , making it a whole of 8 triangle. (REFER TO THE IMAGE ATTACHED)

Now, from the image we can notice that the every two triangles with same base and height as equal area. So let us mark the areas of 8 triangles as p,q,r,s.

Now we know that :

(p+q) + (r+s) = (q+r) + (s+p)

We know that :

(p + q) = 16 ; (r + s) = 32 ; (q + r) = 20

Also it is easy to notice that area that is unknown = (s+p)

So from this we can find that , Unknown area = (16 + 32) - 20

= 28

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Hope my answer is helpful to you.