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In the diagram, PQRS is a trapezoid with an area of 12. RS = 7 and PQ = 28. What is the area of triangle PQS?

 

 Aug 22, 2023
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It looks like  RS should be 28  and PQ = 7

 

Area of  trapezoid =  (1/2)(height of triangle QSR) ( sum of  base lengths)

 

12 =  (1/2)(height of triangle QSR) ( 28 + 7)

 

12 = (35/2)  ( height of triangle QSR)

 

12 ( 2 / 35)  = height of  triangle QSR

 

24/35 =  height of  triangle QSR

 

Area of triangle QSR = (1/2)RS (height of QSR) =  (1/2)(28)(24/35) =  (14/ 35)*24 = (2/5) (24) =  48/5  = 9.6

 

[PQS ] =  area of trapezoid - area of triangle QSR =  12 - 9.6 =  2.4

 

 

cool cool cool

 Aug 22, 2023

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