A geometry problem by Mr X

Geometry Level 3

The figure shows a quadrilateral with all its side lengths given: 30, 9, 13, 28. The line drawn from the top vertex to the bottom side (with length 28) has length 18.

Find the area of this quadrilateral.


Note: The figure may not be drawn to scale.


The answer is 306.

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2 solutions

Mr X
Aug 17, 2017

Here is the beauty of the geometrical solution

Whilst I am impressed with you seeing this, as I did not, this seems like a fluke to me. If the numbers had been slightly different you would not have been able to proceed at all. But I repeat that I was impressed that you saw this. Regards, David

David Fairer - 3 years, 9 months ago

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I agree with you. Each problem has its solution. I wanted is to share a new way of geometrical solutions ...

Mr X - 3 years, 9 months ago

Excellent solution, at least in my unschooled way of thinking. I knew it had to be there somewhere but just couldn't see it. I resorted to using a brute-force method which I would now be embarrassed to post.

John Miller - 3 years, 9 months ago
Relue Tamref
Aug 26, 2017

Using Pythagorean Theorem we can find the sides D C , C A , E D DC, CA, ED for the right triangles we can calculate their areas directly using their height and base, for the A B C \triangle ABC we use Heron's Formula summing those areas give us 306 306

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