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
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