FINDING AREA OF A CUTE AND SIMPLE GEOMETRIC PROBLEM

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(Edited)

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 βˆ†ADO and βˆ†AEO. Let the area of βˆ†ADO and βˆ†AEO be a cm and b cm respectively.

The concept I am going to use as follows:
We know that the area of a βˆ† depends on two things i.e the height and the base of a given βˆ†. 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 βˆ†BDC & βˆ†ADC respectively.

The figure below contains the same element while the triangle are βˆ†CBE and βˆ†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 βˆ†ADC & βˆ†BDC. And in the second equation the same thing is done considering βˆ†AOC & βˆ†ABC.You can check it in the figure below as words may confused you.πŸ˜‚

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 βˆ†

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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24 comments
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Bro, i wish these solutions can fix my life problems too πŸ˜‚πŸ˜‚πŸ€£ JK.

Not really Good at Math.

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In simple mathematics we got limited number of variable but in life an equation of problem got infinite variables. Haha math can't solve them yet. So sorry dude.

Thanks for visiting and making a valuable comment.

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I loved it both at the High School and at the University! Another good math memory!

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I am glad you liked it.

Thanks for visiting man

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I tried to follow, but I notice my geometry skills are a bit rusty! I used to do a lot of algebra in my younger version of me, but that was many years ago.

Very impressive work, though! πŸ‘

!POB
!CCC
!PIZZA

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I also love algebra , I'll bring it on later.

Thanks for visiting dude.

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When you do that let me know, please! I would love to try to refresh my algebra brain. 😎

Have a great weekend!

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Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!

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A very simple explanation, I will give it a try when I am less busy. Thanks for sharing

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I am glad you like it.Yeah it's a easy one ,you can try when you be free.

Thanks for visiting dude.

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🌺This indeed is your Niche Meta, Nicely done, BravoπŸ”₯πŸ”₯

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Thanks for visiting and supporting queenstarr

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There is no photo here but i think the answer is 7 :)

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πŸ˜‚πŸ˜‚πŸ˜‚ This is not a GI question.It's real geometric problem. You can check the solution entering the post.

Thanks for visiting dude.

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Math Hero!
πŸ€“πŸ§ πŸ‘‘πŸŸ

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πŸ˜€πŸ˜€ thanks man

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It's nice to see such mathematics kit joining hive. I'm also a math lover, though I am a trader, I have done my graduation in mathematics.

Keep going bro, nice work.

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Wow! It's good to know that you love mathematics.Thanks for visiting.

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