Question

Find the area of a kite ABCD if BD= 48cm, AB= 25cm, and BC= 26cm?

Answer 1

`S=408cm^2`

Explanation:

The formula of a kite's area is
`S=(1/2)d1*d2`
where
`d1="kite's long diagonal"`
`d2="kite's short diagonal"`

In the problem, be noticed that once the diagonal BD has an endpoint in B (where 2 segments of different sizes, AB and BD, meet), this diagonal is divided in two equal parts by the other diagonal. Calling E the point where the two diagonals intercept each other, we have:
`BD=2*DE=48` => `DE=24`

In the right triangle ABE we can obtain the segment AE
`AB^2=DE^2+AE^2` => `25^2=24^2+AE^2` => `AE=sqrt(625-576)=sqrt(49)=7`

In the right triangle BCE we can obtain the segment CE
`BC^2=DE^2+CE^2` => `26^2=24^2+CE^2` => `CE=sqrt(676-576)=sqrt(100)=10`

In this way we discovered the previously unknown diagonal:
`AC=AE+CE=7+10=17`

Finally,
`S=(1/2)(d1+d2)=(48+17)/2=408cm^2`