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