Question

9. In the given figure, PQRS is a quadrilateral. If QR = 18
cm and PS = 9 cm, then what is the area (in cm2) of
quadrilateral PQRS ?
दी गई आकृति में, PQRS एक चतुर्भुज है। यदि QR = 18 से.मी.
तथा 5-9 से.मी. है तो चतुर्भुज PQRS का क्षेत्रफल (से.मी.'
में ) क्या होगा?
plz solve ​

Answer 1

135√3/2 is the area of Quadrilateral

Step-by-step explanation:

∠P + ∠Q + ∠R + ∠S = 360°

=> 150° + 60° + 60°  + ∠S = 360°

=> ∠S = 90°

Lets extend  QP & RS to meet at A

=> ΔQAR will be Equilateral Triangle

QR = 18 cm

Area of ΔQAR  =  (√3 / 4)18²  = 81√3

in Δ PAS    

∠PSA = 180° - 90° = 90°

∠SPA  = 180° - 150° = 30°

Tan 30 = AS/PS

=> 1/√3  = AS/9

=> AS = 3√3

Area of Δ PAS     = (1/2) * 9 * 3√3  = 27√3/2

area of quadrilateral PQRS = Area of ΔQAR - Area of Δ PAS  

81√3 -  27√3/2

= 135√3/2

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