Question

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?

Answer 1

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`.