ABCD is a rectangle, with AP = PQ = QB and points R, S, T dividing the side CD i

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ABCD is a rectangle, with AP = PQ = QB and points R, S, T dividing the side CD in four equal parts. Find the area of the shaded region if the area of the rectangle is A sq. units..

Options:

A .

\frac{A}{12}

B .

\frac{2 A}{9}

C .

\frac{A}{8}

D .

\frac{A}{4}

Answer: Option C
:
C

We know that the area of all triangles between two parallel lines and having a common base is the same

Thus, the triangle can also be represented as follows

we can say that, area (RQS) = area (RR1S)
Using the concept of graphical division, we can divide the figure into 8 equal regions as follows.

The required region is $\frac{A}{8}$ units.

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