SOLUTION: I'm a student of MSciEd secondary math.. I just wanna ask if you could answer the problem set that my instructor in mathed 235 haave given us.. the question is Let ABCD be trapezo

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Question 1107833: I'm a student of MSciEd secondary math.. I just wanna ask if you could answer the problem set that my instructor in mathed 235 haave given us.. the question is
Let ABCD be trapezoid with the sides AD and BC parallel to each other and perpendicular to AB. moreover, assume that BC=2AD. the points P and Q on the side of AB divide it into three equal segments, and P is between A and Q. Similarly, the points R and S on the side of CD divide it into three equal segments, and R is between D and S. Let a1 be the area of the triangle, triangle AQR and let a2 be the area of the triangle, triangle PBS. Find the ratio a1/a2.
Answer by math_helper(2461) (Show Source):
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Area a1 = area of AQR
Area a2 = area of PBS
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Base_AQR = (2/3)AB
Base_PBS = (2/3)AB
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The heights are measured along a line parallel to the x-axis, and note that the projection of DR onto the x-axis has length equal to (1/3)AD, while the projection of SD onto the x-axis has length (2/3)AD.
Height_AQR = AD + (1/3)AD = (4/3)AD
Height_PBS = AD + (2/3)AD = (5/3)AD

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Area_a1 = (1/2) (2/3)AB * (4/3)AD
Area_a2 = (1/2) (2/3)AB * (5/3)AD
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Answer: Area_a1/Area_a2 = 4/5
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