Question

quadrilateral PQRS is a rectangle, PQ+QR=7,PR+PS=10.Find area of PQRS

Answer 1

1) <PQR is a right angled triangle.
PQ is the base and QR is the height.

Area of Δ PQR = 1/2 x PQ x QR
= 1/2 x 7 x 6
= 21 cm2.

Also, PR2 = PQ2 + QR2
PR2 = 72 + 62
PR2 = 49 + 36
PR2 = 85

<PQR is a right angled triangle.
⇒ PR2 = PS2 + SR2
⇒ 85 = PS2 + 22
⇒ PS2 = 81
⇒ PS = 9

SR is the base and PS is the height.

Area of Δ PSR = 1/2 x SR x PS
= 1/2 x 2 x 9
= 9 cm2.

Total area of the quadrilateral = 21 + 9 = 30 cm2.

Answer 2

Here your answer:
Note:-The sum of any two sides of a traingle is greater than other measure of third side.

In PQRS, PS=RQ
So RQ+PR also=10 unit(or cm or m etc..)
PQ+RQ=7unit.........(Given)
RQ=7-PQ........(1)
RQ=10-PR..........(2)

From (1) and (2)
7-PQ=10-PR
PR-PQ=3
PR=3+PQ........(A)
According to (A) PR should be 3 unit greater than PQ,
and according to (1) and (2)
RQ+PR=10 unit
RQ+PQ=7 unit
and according to above NOTE RQ+PQ >PR.
RQ in (1) and (2) will be same measure.
And it will be 4 unit,so that PR=6 and PQ=3.
These unit is must beacuse According to (1),(2) and (A).

PR=3+PQ

lets verify:-
PQ+RQ>PR
3+4>6
7>6
case verified

Case (A)
PR=3+PQ
PR=6
6=6

So all case can be verified.(do another on your own, i did it)
You will find all sides and after finding sides you will get area.


THANKS
HOPE IT HELPS.