Question

Calculate the area of the quadrilateral PQRS shown in the
adjoining figure, it being given that PR = 8 cm, RQ = 17
cm,Angle RPQ = 90°, RS = 6 cm and Angle PRS = 90°.​

Answer 1

Answer:

area of quadrilateral is 105 sq cm

Answer 2

The area of the quadrilateral PQRS is 105 $(cm^{2})$.

Step-by-step explanation:

1. Given data

  PQ = 8 cm

  QR =17 cm

  RS =6 m

2. As $\Delta PQR$ is a right angle triangle , right angle is at point P. So RQ is hypotenuse of $\Delta PQR$ .

   From Pythagoras

  $PR^{2}= RQ^{2}-PQ^{2}$

  $PR^{2}= 17^{2}-8^{2}$

 So

 PR = 15 cm

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

4. Area of quadrilateral PQRS = area of $\Delta PQR$ + area of $\Delta PSR$        ...1)

5. Area of $\Delta PQR$ = $\frac{1}{2}\times PR\times PQ$   ...2)

6. Area of $\Delta PSR$ = $\frac{1}{2}\times PR\times RS$   ...3)

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

  Area of quadrilateral PQRS = area of $\Delta PQR$ + area of $\Delta PSR$

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

8. Equation 4) can be written as

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

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

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

 So

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