This is from GregMat’s practice problems. For this problem, I calculated the area of one of the hypotenuses of the identical triangles and got approx 5.66 (I did decimals instead of square roots bc the answer choices were in decimals). Then I subtracted 4 from the hypotenuse to get the length of the hypotenuse of the tiny triangle at the bottom of quadrilateral DECF, which was 1.66. After using pythag’s theorem to solve for the sides of the mini triangle, I got .91 for each side. I then multiplied the length of the hypotenuse 5.66 by .91 and then added the area of the mini triangle .42 (.91 x .91 = .83/2 = .42) to get 5.57, which was not close to any of the answers.
Can someone explain why this method is flawed? I saw greg’s explanation video, but if I came across this question on the actual exam, my first reaction would be to approach it the way I explained earlier, which concerns me if this is the wrong way to think about it. I never would have thought to set it up as greg’s way on my own.
