SOLUTION: in the figure above, P is the midpoint of AB and Q is the midpoint of BC. If the area of trapezoid APQC is 20, what is the area of triangle ABC.

Question 1195284: in the figure above, P is the midpoint of AB and Q is the midpoint of BC. If the area of trapezoid APQC is 20, what is the area of triangle ABC.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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in the figure above, P is the midpoint of AB and Q is the midpoint of BC.
If the area of trapezoid APQC is 20, what is the area of triangle ABC.
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Trapezoid AQPC is the triangle ABC with triangle PCQ cut from it.


Triangle PCQ is similar to triangle ABC with the similarity coefficient 1/2
from smaller to larger.


Therefore, the area of triangle PCQ is 1/4 of the area of triangle ABC.


So, if area of triangle PCQ is x, then the area of triangle ABC is 4x.


Next, from the given part we have this equation

    4x - x = 20 square units,

which gives us

       3x  = 20,  x = 20/3.


Therefore, the area of the triangle ABC is

       4x =  =  = 26  = 26.666...  = 26,667 square units, rounded.    ANSWER

Solved.

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