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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
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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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