Can you find the area?

Geometry Level 1

HEY!! suppose that, ABCD is a rectangle. E , F are the midpoints of side AD and CD respectively.If the AREA of quadrilateral EBFD is 9.What is the area of the rectangle ABCD ?


The answer is 18.

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2 solutions

Shamin Yeaser
Sep 28, 2017

Thank you so much for appreciating my effort! HERE is how to crack it: since ABCD is a rectangle,the opposite sides are equal.thus AB=CD and BC=AD . Now,let's consider AB=CD=x and BC=AD=y .so the area of the rectangular is xy .
The area of EBFD=xy- 1 2 \frac{1}{2} . x 2 \frac{x}{2} .y- 1 2 \frac{1}{2} . y 2 \frac{y}{2} .x
or, 9=xy-( x y 4 \frac{xy}{4} + x y 4 \frac{xy}{4} )
or, 9=xy- x y 2 \frac{xy}{2}
or, 9= x y 2 \frac{xy}{2}
or, xy=9*2=18.and xy is the area of the rectangle.

Samir Betmouni
Oct 7, 2017

Since F is the midpoint of CD, triangles CFB and FBD have equal bases and equal heights. So they have equal area.

Similarly, triangles DEB and AEB have the same area.

FBD and DEB add up to 9. So their partners add up to 9. Making a total of 18 for the whole rectangle.

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