SOLUTION: PQRS is a trapezium where PQ // SR. Given that PQR = SPR= 90˚, PQ = 8.5cm and PR = 12.3 cm. Calculate (a) QR (b) PS (c) The area of the trapezium PQRS.

You must be from the UK. In the US we say "trapezoid" and "math",
and you say "trapezium" and "maths".  :)



We can find QR by the Pythagorean theorem:













Angles QPR and PRS are equal in measurement because they are alternate
interior angles formed by transversal PR intersecting two given parallel
line segments PQ and SR. And we are given that PQR = SPR = 90˚.  Therefore,
right triangles PQR and RPS are similar triangles.  Therefore their
sides are proportional, so we set up the proportion:




So:

 



Solve that proportion equation and get  



We find the areas of both triangles and add them.

To find the area of triangle PQR, we use formula





To find the area of triangle RPS, we use formula





Adding those areas together:



Edwin