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?
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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(52799) (Show Source):
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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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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.
