In the diagram, $PQRS$ is a trapezoid with an area of $32.$ $RS$ is twice the length of $PQ.$ What is the area of $\triangle PQS?$
Triangles PQS and RQS are under the same height.....and triangles under the same height are to each other as their bases
So area of triangle RQS = 2 * the area of triangle PQS
[ PQS ] + [ RQS] = area of trapezoid....so.....
[PQS ] + 2 [ PQS ] = 32
3 [ PQS ] = 32
[ PQS ] = 32 / 3