Question

find the area of the shaded region in the adjoining figure given that PS =11cm,QR = 19cm,RS =17 cm and angle SPQ = angle PQR = 90 degree​

Answer 1

Answer:

Let the name of the Rectangle be PQAS

Now, SP = AQ {Opposite Side of the Rectangle}

=> AQ = 11cm.

=> AR = 19 - 11 = 8 cm.

Since SA || PQ, RQ as the transversal <RAS = <AQP (Corresponding angles)

In ∆ RSA,

Applying Pythagoras,

AS²= RS²- AR²

AS = √289 - 64

= √225 = 15 cm.

=> Area Of The Triangle RSA = ½ . AS . RA

= ½ . 15 . 8

=60 cm²

Now, For Rectangle AQPS,

Area (Rectangle) = L.B

= 11 × 15 = 165cm²

Adding Areas Of The Rectangle and the Triangle :

60cm² + 165cm² = 225cm²//