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# In the figure given below, ABCDEF is a regular hexagon of side length 1, AFPS and ABQR are squares.Then the ratio Area (APQ)/ Area (SRP) equals

Sandeep Pathak
askIITians Faculty 25 Points
6 years ago
Notice length of AP == length of AQ.
Also note
and length of SR = length of SP = 1.

so the two triangles are iscosceles with same angle between the equal sides. So the ratio of areas is equal to square of ratio of equal sides. This gives

Vineeth
19 Points
6 years ago
Sir , can you explain this answer with more steps.
Sandeep Pathak
askIITians Faculty 25 Points
6 years ago
length of AP and AQ isas these are diagonals of square with side 1.
Since AP and AQ are diagonals of square ASPF and ABQR respectively

Also, due to hexagon property, angle between adjacent sides is, so
Now, consider triangle RAS.

Similarly other angles can be proved to be equal and this triangle RAS is an equilateral triangle. So, RS = AS = SP = 1.
Now, in triangle RSP,


Hope the steps are clear to you. In future, I would suggest if something is not clear in the solution, please specify what exactly you were not able to understand so that We can provide answers that can help in a better way. Cheers!