In the diagram, PQRS is a trapezoid with an area of 12. RS is twice the length of PQ. What is the area of \(\triangle PQS?\)

tertre
Apr 18, 2017

#1**+2 **

Note that triangle PQS has the same height as triangle QRS

And triangles under the same height are to each other as their bases...

So....since RS = 2PQ.....then the area of triangle QRS = 2 area of triangle PQS

So area of QRS + area of PQS = 12 substituting......we have

area [ 2PQS + PQS ] = 12

area [ 3PQS ] = 12 divide both sides by 3

area PQS = 4

CPhill
Apr 18, 2017