Question

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

Answer 1

given that

ABCD is a square
and diagonals intersect at  o
in a square diagonals bisect each other
soo it dives into 4 congruent triangles

requried :
 ar( abcd ) : ar ( aob ) = ???

solution :

1 triangle is 1/ 4 of square soo
   ratio of that is  1 : 4
           ar ( aob ) = 1
           ar ( abcd ) = 4

soo 1 : 4






hope this helped u . plzz mark my answer as the best one plzzz

Answer 2

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