SOLUTION: In the given figure, the two rectangles EFGH and ACDE share a common corner at E and overlap so that BC = 7. What is the area of the shaded region ABGFEA? Image is in the link:

Question 1061956: In the given figure, the two rectangles EFGH and ACDE share a common corner at E and overlap so that BC = 7. What is the area of the shaded region ABGFEA?
Image is in the link: http://prntscr.com/dkzrj8
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
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In the given figure, the two rectangles EFGH and ACDE share a common corner at E and overlap so that BC = 7.
What is the area of the shaded region ABGFEA?
Image is in the link: http://prntscr.com/dkzrj8
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I just solved this problem yesterday. See the link
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1061892.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1061892.html

For your convenience, I copy, past and place this solution here again:
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1.  Consider the quadrilateral ABHE (which is the intersection area of the original rectangles).  Notice that |AB| = 8 - 7 = 1 unit long.


2.  Draw the diagonal BE in this quadrilateral.

    The length of the diagonal BE is  |BE| =  =  = .


3.  Therefore, the length of the segment BH is  |BH| =  =  =  = 9.


4.  The area of the triangle ABE is  =  = 6.

    The area of the triangle BHE is  =  = 36.


    Hence, the area of the quadrilateral ABHE is the sum of the areas of the triangles 6 + 36 = 42.


5.  Now the area of the shaded part under the question is 12*8 - 42 = 96-42 = 54.

Answer. The area of the shaded region ABGFEA is 54 square units.

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