Missing area of a square with no given dimensions

[Kuldeep Matharu]

Ignoring all the decimal numbers, your drawing does suggest a nice way to see the key idea:

View attachment 33119​

Each of the four triangles is clearly half of the rectangle containing it (e.g. HIJE), so the sum of the greens, and the sum of the reds, are both exactly half of the area of EFGH. This implies that the sum of opposite regions in the original drawing is half of ABCD, so that area is 96, and we can see the missing area.

Also, from that, we could work out the areas of the individual triangles, and the location of P, in a different way than I did before (which used triangles PEG and PHF).

Thanks

 

[Kuldeep Matharu]

Ignoring all the decimal numbers, your drawing does suggest a nice way to see the key idea:

View attachment 33119​

Each of the four triangles is clearly half of the rectangle containing it (e.g. HIJE), so the sum of the greens, and the sum of the reds, are both exactly half of the area of EFGH. This implies that the sum of opposite regions in the original drawing is half of ABCD, so that area is 96, and we can see the missing area.

Also, from that, we could work out the areas of the individual triangles, and the location of P, in a different way than I did before (which used triangles PEG and PHF).

I must appreciate for your taking interest in these geometrical shapes the geometry behind it thanks you sir