Question

If we have a quadrilateral PQRS where <PQR=<PRS-90°given that PR-9.2m
a) Length of PQ
Answe
b) Length of QR
c) lenght of PS
d) lenght of RS
e) perimeter of PQRS
f) area of PQRS​

Answer 1

Answer:

As ΔPQR is a right angle triangle , right angle is at point P. So RQ is hypotenuse of \Delta PQRΔPQR .

From Pythagoras

PR^{2}= RQ^{2}-PQ^{2}PR

2 =RQ 2 −PQ 2

PR^{2}= 17^{2}-8^{2}PR

2 =17 2 −8 2

So

PR = 15 cm

From figure, it is clear that SR is perpendicular to PR and PQ is perpendicular to PR.

Area of quadrilateral PQRS = area of \Delta PQRΔPQR + area of \Delta PSRΔPSR ...1)

Area of \Delta PQRΔPQR = \frac{1}{2}\times PR\times PQ 21 ×PR×PQ ...2)

Area of \Delta PSRΔPSR = \frac{1}{2}\times PR\times RS 21 ×PR×RS ...3)

From equation 1, 2 and 3, equation 1) can be written as

Area of quadrilateral PQRS = area of \Delta PQRΔPQR + area of \Delta PSRΔPSR

Area of quadrilateral PQRS=\frac{1}{2}\times PR\times PQ + \frac{1}{2}\times PR\times RS 21 ×PR×PQ+ 21 ×PR×RS ...4)

Equation 4) can be written as

Area of quadrilateral PQRS =\frac{1}{2}\times PR\times (PQ+RS)= 21 ×PR×(PQ+RS)

Area of quadrilateral PQRS =\frac{1}{2}\times 15\times (8+6)= 21 ×15×(8+6)

Area of quadrilateral PQRS =\frac{1}{2}\times 15\times (14)= 2×15×(14)

So

Area of quadrilateral PQRS =15\times 7=105(cm^{2})=15×7=105(cm2 )

Step-by-step explanation:

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