What happens to the area of a kite if you double the length of one of the diagonals? Also what happens if you double the length of both diagonals?

1 Answer
Jan 22, 2016

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#.