Area of a quadrilateral solved with trig
So this is another one from Bostock and Chandlers Core A-Level Maths:
In a quadrilateral PQRS, PQ=6cm, QR = 7cm, RS = 9cm, PQR=115 and PRS=80.
Find the length of PR, then considering it split into two separate triangles find the area of PQRS.
The area of PRQ
So then I look for the angle QRP
This means the angle PRS = 80-29.68 = 50.32
I then use this angle to find the area of the other half PRS
finally add the two halves together giving:
The book says the answer is 67.7 or 67.8 (allowing for rounding)
So the question is why am I so far out... I've went through my workings a couple of times now and cannot see where I am going wrong.
Any help appreciated