I am honestly pleasantly surprised this thread was very supportive … a rare find in EDMW, thanks to those who shared their working.
I myself actually made a careless mistake
to overlook that EK = KL … and once factor in this + the cut through K is in the middle of HG, the same-sized-square-below-EFGH makes sense now … and if we turn triangle EHK clockwise down using K as the swivel point into the same-sized-square below, it would = triangle GKL … which would make triangles ELH (and JEH) each = 1/2 * 13 * 13 = 84.5, which settles Question 1.
And even if we don’t calculate triangle HKL directly on its own, we can calculate EHK = 1/2 * 6.5 * 13 = 42.25 which would make HKL = 84.5 - 42.25 = 42.25 … which gives us the total area of the figure = 169 + 84.5 + 42.25 = 295.75, which settles Question 2.
Unfortunately the person who told my kid that EHK = HKL so EHK * 2, did not actually explain why it was * 2
I myself actually made a careless mistake
to overlook that EK = KL … and once factor in this + the cut through K is in the middle of HG, the same-sized-square-below-EFGH makes sense now … and if we turn triangle EHK clockwise down using K as the swivel point into the same-sized-square below, it would = triangle GKL … which would make triangles ELH (and JEH) each = 1/2 * 13 * 13 = 84.5, which settles Question 1.And even if we don’t calculate triangle HKL directly on its own, we can calculate EHK = 1/2 * 6.5 * 13 = 42.25 which would make HKL = 84.5 - 42.25 = 42.25 … which gives us the total area of the figure = 169 + 84.5 + 42.25 = 295.75, which settles Question 2.
Unfortunately the person who told my kid that EHK = HKL so EHK * 2, did not actually explain why it was * 2
