Question 1186474
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ABCD is a square with side of 10 cm. {{{highlight(cross(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.
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<pre>
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  {{{sqrt(36)}}} = 6.


Since the trapezoids are equal (congruent), it means that the strip between the squares is of uniform width of  {{{(10 - 6)/2}}} cm = {{{4/2}}} = 2 cm.


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


<U>ANSWER</U>.  The height of the trapezoids is 2 cm.
</pre>

Solved.



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These words in the condition of the problem


<pre>
    {{{highlight(cross(3_points))}}} Square PQRS 
</pre>

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