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

Step-by-step solution

In APQ AP = AQ = 2 , APQ =30^ In SRP S R=S P=1 , R S P=30 ^ FAB =120^ B A S = F A B - F A S =120^ -90^ =30^ S A R = B A R - B A S =60^ In A R S array l 60^ = 1+1- SR ² 2.1 .1 [ AR = AS =1] SR =1 array Now, RSP = ASP - ASR =90^ -60^ =30^ [ ASR is equilateral] Now, from SRP RP = 3 -1 2 2 In APR RAP = ( 2 )²+1²-P R² 2 2 RAP =15^ PAQ = RAQ - RAP =45^ -15^ =30^ Now, ar ( APQ ) ar ( SRP ) = 1 2 2 2 30^ 1 2 1 1 30^ =2