FINDING AREA OF A CUTE AND SIMPLE GEOMETRIC PROBLEM

Hello math bugs(🐞) and hivers(🐝)
I hope you are strong and stout and doing great in life.

Once again I am back with another geometric problem.To prepare all the figures and and solution I did my best.You must have seen the problem in the cover photo.Check the problem once again and try to solve the it. Then step forward to the solution.

I have seen people have less interest to find solution.My moto is to convince them visualising the problem. That's why I always makes the figure colourful.If people do not like my work, hard work will be worthless. Let's see how people react to the article.

The first step is to draw a line as you can see it below in white color and thus the quadrilateral ADOE gets divided into two part i.e ∆ADO and ∆AEO. Let the area of ∆ADO and ∆AEO be a cm and b cm respectively.

The concept I am going to use as follows:
We know that the area of a ∆ depends on two things i.e the height and the base of a given ∆. The beauty of the concept is when height (perpendicular distance) equals, the ratio of bases becomes the ratio of area of the triangles.Check it in the figure below:

In the above figure raito of the sides BD & AD is equal to the ratio of area of ∆BDC & ∆ADC respectively.

The figure below contains the same element while the triangle are ∆CBE and ∆ABE.

Solution as follows:
You can see two equation in the figure below.Both of them are made using the concept I mentioned in previous figure or in point.In the first equation ratio of AD & BD equals to the ratio of area of ∆ADC & ∆BDC. And in the second equation the same thing is done considering ∆AOC & ∆ABC.You can check it in the figure below as words may confused you.😂

I solved the problem using just triangle property.
There are others ways also to solve it
.

let's say mass point geometry. This concept can make it easier but many may not aware of it so I avoided it.If you want to know mass point geometry for a easier solution, make a comment right below the post.

Time for visualising our answer below:

Some links of my previous articles you may like them

Problem on angle bisectors of a ∆

Finding angle using median

Ortho-centre(no circle)

Centroid/geo-centre(Medians)

In-centre(In-circle)

Cir-centre(cir-cum-circle)

I hope you liked today's problem and the solution.

Thank you for so much for visiting.

Have a nice day

All is well

Regards: @meta007

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