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In the diagram, $PQRS$ is a trapezoid with an area of $32.$ $RS$ is twice the length of $PQ.$ What is the area of $\triangle PQS?$

 

 Mar 25, 2021
 #1
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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

 

So

 

[ PQS ] + [ RQS]   = area of  trapezoid....so.....

 

[PQS ] + 2 [ PQS ]  =   32

 

3 [ PQS ]  = 32

 

[ PQS ] = 32 /  3

 

cool cool cool

 Mar 25, 2021
 #2
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+1

Area of triangle PQS = 1/3(32)

 Mar 25, 2021

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