The area of a kite is given by ##A=(pq)/2##

Where ##p,q## are the two diagonals of the kite and ##A## is the area of he kite.

Let us see what happens with the area in the two conditions. ##(i)## when we double one diagonal. ##(ii)## when we double both the diagonals.

##(i)## Let ##p## and ##q## be the diagonals of the kite and ##A## be the area. Then ##A=(pq)/2##

Let us double the diagonal ##p## and let ##p’=2p##. Let the new area be denoted by ##A’## ##A’=(p’q)/2=(2pq)/2=pq##

##implies A’=pq##

We can see that the new area ##A’## is double of the initial area ##A##.

##(ii)##

Let ##a## and ##b## be the diagonals of the kite and ##B## be the area. Then ##B=(ab)/2##

Let us double the diagonals ##a## and ##b## and let ##a’=2a## and ##b’=2b##. Let the new area be denoted by ##B’## ##B’=(a’b’)/2=(2a*2b)/2=2ab##

##implies B’=2ab##

We can see that the new area ##B’## is four times of the initial area ##B##.