Question

ABCD is a square whose diagonals intersect at O.
Calculate ar(angle AOB): ar (ABCD).

Answer 1

SOLUTION:-

square is a type of parralelogram 
means its diagonals bisect each other and diagonal cut it into tris of equal area
so 
ar abcd=ar abc + ar acd
ar abcd=2 ar abd 
ar abd = ar aob+ ar boc 
also ar aob = ar boc as bo is median 
ar abcd =2*2 ar aob
ar abcd = 4 ar aob
ar abcd:ar aob
1:4