SOLUTION: ABCD is a square with side of 10 cm. 3 points Square PQRS is drawn inside the square ABCD such that trapezoids PQBA, QRCB, SRCD and PSDA are equal. If the area of the trapezoid is

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Question 1186474: ABCD is a square with side of 10 cm. 3 points Square PQRS is drawn inside the square ABCD such that trapezoids PQBA, QRCB, SRCD and PSDA are equal. If the area of the trapezoid is 16 cm^2, find the height of the trapezium.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here is a partial diagram of the figure....



The area of trapezoid SRCD is 16:









or

Obviously from the diagram the x we want is x=2.

ANSWER: the height of the trapezoid is 2cm.

NOTE: The solution from tutor @ikleyn, using the fact that the four trapezoids are congruent, is much easier than my solution above....
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
ABCD is a square with side of 10 cm. Square PQRS is drawn inside the square ABCD
such that trapezoids PQBA, QRCB, SRCD and PSDA are equal.
If the area of the trapezoid is 16 cm^2, find the height of the trapezium.
~~~~~~~~~~~~~~~~~~ 


From the area of the square ABCD, subtract four times the area of the trapezoid to get the area of the square PQRS


    the area of the square PQRS = 10^2 - 4*16 = 100 - 64 = 36 cm^2.


Hence, the side of the square PQRS is   = 6.


Since the trapezoids are equal (congruent), it means that the strip between the squares is of uniform width of   cm =  = 2 cm.


The width of the strip is the height of the trapezoids.


ANSWER.  The height of the trapezoids is 2 cm.

Solved.


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These words in the condition of the problem 

     Square PQRS

perplexed me, when I read this problem today in the morning . . .




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