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

Answer 1

#S=408cm^2#

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#

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Answer 2

Caroline Aucoin

To find the area of a kite, you can use the formula: Area = (diagonal1 * diagonal2) / 2.

Given that BD = 48 cm and AB = 25 cm, and BC = 26 cm (which is also a diagonal), we can use the diagonals BD and BC.

So, Area = (48 * 26) / 2 = 1248 square centimeters.

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Answer from HIX Tutor

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