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

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




cool cool cool

CPhill  Apr 18, 2017
edited by CPhill  Apr 18, 2017

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