SOLUTION: An envelope is pictured below. Solve for the area of the shaded region. https://ibb.co/v4zLj1sc

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Question 1210156: An envelope is pictured below. Solve for the area of the shaded region.
https://ibb.co/v4zLj1sc
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
An envelope is pictured below. Solve for the area of the regions
marked XXX.



DE is half of 12 or 6. So we find AD with the Pythagorean theorem.
(Or you may recognize it as a 6-8-10 right triangle, a 3-4-5 right triangle
with all sides doubled):

AD+=+sqrt%28AE%5E2-DE%5E2%29+=sqrt%2810%5E2-6%5E2%29+=+sqrt%28100-36%29+=+sqrt%2864%29+=+8 

So tha area of right triangle ADE is expr%281%2F2%29%2Abase%2Aheight%22%22=%22%22
expr%281%2F2%29%2ADE%2AAD%22%22=%22%22expr%281%2F2%29%2A6%2A8%29%22%22=%22%2224in2.

Triangle BCE is congruent to triangle ADE so it also has area 24in2. 

Total shaded area (or area marked XXX) = (2)(24) = 48 in2.

Edwin