So this is another one from Bostock and Chandlers Core A-Level Maths:

The Question

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.

My Solution

so

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