The Elegant Bird: Heron

Geometry Level 4

What is the area of the triangle shown in the above figure?

The figure above is not to the scale.
Not possible to find. 12.67 12.67 0 0 12.33 12.33

Nihar Mahajan by Nihar Mahajan , 20, India

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2 solutions

Nihar Mahajan
May 9, 2016

Since 6 + 3 = 9 6+3=9 , the triangle so formed is a "degenerate" triangle or a line segment with 3 collinear points, hence, its area is zero: 0 \boxed{0} . (You can also verify that the area is 0 0 by substituting the values in Heron's formula :) )

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Great observation.

Next question is what the area of the triangle is on a spherical plane.

Sharky Kesa - 5 years ago

And this problem is sure to rise debates .... BTW (+1)

Edit: Lol !! Guess what ( Reports)..

Rishabh Jain - 5 years, 1 month ago

Log in to reply

I know, one report has already been posted.Surprising to see a guy level 5 in so many subjects, not knowing about a degenerate triangle.

Nihar Mahajan - 5 years, 1 month ago

By the law of cosines, we have

9 2 = 6 2 + 3 2 − 2 ( 6 ) ( 3 ) ( cos ⁡ A ) 9^2=6^2+3^2-2(6)(3)(\cos A)

A = 18 0 ∘ A=180^\circ

Therefore, the area of the triangle is zero.

1 Helpful 1 Interesting 1 Brilliant 0 Confused

Nice solution.

Marvin Kalngan - 1 year, 1 month ago

1 pending report

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