PQRS is a Trapezium

Question

PQRS IS A TRAPEZIUM WHERE PQ ARE PARALLEL TO SR.

GIVEN THAT PQR=SPR=90 DEGREES , PQ=8.5 CM AND PR=12.3 CM

CALCULATE

A)QR

B)PS

C)THE AREA OF THE TRAPEZIUM PQRS

Answer 1

QR = sqrt(12.3^2-8.5^2)

 

     = 8.89 cm

 

angle RPQ = tan (8.89/8.5)= 46.26 degrees

 

So, angle PRS = 46.26 degrees.

 

Say PS = x

 

x/12.3=tan (46.26)

 

x= 12.85 cm

 

RS = sqrt(12.85^2+12.3^2)

 

RS = 17.78 cm

 

AREA Of THE TRAPEZIUM= 0.5(8.5+17.78)*8.89

 

                                      =116.81 sq cm