Question

find the area of a quadrilateral whose one diagonal is 10 cm and altitude to the diagonals from the opposite vertex are 6 cm and 4 cm . find its area​

Answer 1

Yes! we CAN find the area of this QUADRILATERAL

SO, LETS BEGIN♡◇
First of all, we need to know how to draw the diagram correctly

So for that read below
》》 It is said ' Find the area of quadrilateral'
So, we need to draw a quadrilateral first.
And Then,it is said ' diagonal is 10cm...
So, draw a diagonal by joining any two opposite vertex of the figure....
CONGRATS!
You have almost made the figure...
Now the most confusing words are said ,'Altitude from opposite vertex are taken ... which are 4 and 6cm respectively... u can take anyone of them as 4 0r 6 CM....
We have made the figure at last....
( As we see in the attachment)
Now turn of solving the question....
$we \: can \: clearly \: see \: here \: that \: two \: triangles \: are \: formed \: here \: that \: are \:$
Triangle ADB and BCD
So,
$ar(adb) = \frac{1}{2} \times base \times height$
$= > ar(adb) = \frac{1}{2} \times 10 \times 6$
$= > ar(abd) = 30 {cm}^{2}$
We found area of ADB .... So now find area of BCD ..
$ar(bcd) = \frac{1}{2} \times base \times height$


$= > ar(bcd) = \frac{1}{2} \times 10 \times 4$
$= > ar(bcd) = 20 {cm}^{2}$
So, Now combining both the areas we will get area of ABCD...
So,
$30 {cm}^{2} + 20 {cm}^{2} = 50 {cm}^{2}$
Therefore
$area \: of \: abcd = {50cm}^{2}$