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if a parallelogram or trapezium PQRS , PQ=24 cm PS = 8 cm the perpendicular is from P to S as PM right angle.

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3 Answers

I will try to figure out the diagram from the description.
 
We have a parallelogram PQRS
PQ=24 cm and therefore RS=24 cm
PS=8 cm and therefore QR=8 cm
a line segment is drawn from point P perpendicular to line segment SR at point M; this is line segment PM which is 7 cm
another line segment is drawn from point P perpendicular to segment QR and which bisects QR
let's call this segment PT
therefore QT=4 cm and TR=4 cm
we are trying to find "x"
if x is a line segment, then there are only three line segments that we don't know the value of
we don't know the value of segment PT, segment RM, and segment MS
so let's find all these values
triangle PQT is a right triangle whose hypotenuse is PQ
if PT is x we have 24^2=4^2+x^2
                              576=16+x^2
                              560=x^2
                              x=23.6643 cm
triangle PSM is a right triangle whose hypotenuse is PS
if SM is x we have 8^2=7^2+x^2
                                 64=49+x^2
                                 15=x^2
                                   x=3.87298 cm
if MR is x we have SR-SM=24-3.87298=20.127 cm
if "x" is an area, we have the area of triangle PQT with base 4 cm and height 23.6643 cm which is easy to find
we have the area of triangle PSM whose base is 3.87298 and whose height is 7 cm which is easy to find
we have the area of quadrilateral PTRM which is the area of the parallelogram(with base 24 cm
and height 7 cm) minus the areas of the triangles PQT and PSM
 
 
Not sure i am understanding the description you gave....
1) A parallelogram has parallel sides
2) A Trapezium has no parallel sides
 
So it can't be both.....i think you mean that the shape you describe could be either one.  Assuming that is true, then i need more help in understanding the picture.
 
I am not following the description you give of the figure, can you upload an image?  If not, start by describing the shape, or how to draw the shape.....For example:
 
a 4 sided polygon, with vertices PQRS 
angle PQR is acute but unknown
angle QRS is obtuse but unknown
angle RSP is 90
angle SPQ is 90
 
There is a perpendicular drawn from P to QR which bisects QR and is perpendicular to QR
 
 
In your explanation above, i have no idea where the point M is, or what it should look like.....maybe say something like:
 
Point M is on the segment SR such that PM is perpendicular to SR
 
 
Not sure i have it all right but hopefully you get the idea.
 
Thanks
Surprise!!! I left the comment, but it does not appear above .... Here it is: 

"Zafar, help us to help you, or better serve you. Copy the problem exactly as it appear in the original source and not your own interpretation. What you typed makes no sense whatsoever. First of all parallelogram and trapezoid are two different geometrical figures. Second, what is "x"?" 

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