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Originally posted by LinkbladeNow if you want you can get an extra point by demonstrating that SPOILER the space due to the different form of the triangles equals exactly one rectangle
a=side length of one square
surface area of imagined big triangle Abig=(5a*13a)/2=32,5a^2
surface area of blue triangle Ablue=(2a*5a)/2=5a^2
surface area of red triangle Ared=(3a*8a)/2=12a^2
surface area of yellow and green shape Ayegr=3a*5a=15a^2
surface area of actual quadrangle shape Aquad=Ablue+Ared+Ayegr=(5+12+15)a^2=32a^2
the space between the imagined big triangle and the actual quadrangle shape is
space=AbigAquad=32,5a^232a^2=0,5a^2
Since along the slope both A and B differ from the imagined big triangle by 1*space each, the total difference between A and B along the slope is
2*space=2*0,5a^2=1a^2 quod erat demonstrandum
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