HF RL Explorer

Task 362

Task 362: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. The square quilt block shown is used in a larger quilt. The four small squares in the block are congruent, and the four small vertical rectangles in the block that are not squares are also congruent. The…

The task

The square quilt block shown is used in a larger quilt. The four small squares in the block are congruent, and the four small vertical rectangles in the block that are not squares are also congruent. The total area of the shaded regions is what fraction of the total area of the block? Express your answer as a common fraction. [asy] fill((-10,0)--(-5,0)--(-5,5)--cycle,gray(0.7)); fill((-5,5)--(-5,10)--(0,10)--cycle,gray(0.7)); fill((0,0)--(0,10)--(10,10)--cycle,gray(0.7)); fill((0,0)--(-10,-10)--(0,-10)--cycle,gray(0.7)); fill((0,-10)--(5,-10)--(5,-5)--cycle,gray(0.7)); fill((5,-5)--(5,0)--(10,0)--cycle,gray(0.7)); draw((10,10)--(10,-10)--(-10,-10)--(-10,10)--cycle); draw((-10,-10)--(10,10)); draw((0,10)--(0,-10)); draw((10,0)--(-10,0)); draw((-5,0)--(-5,10)); draw((5,0)--(5,-10)); [/asy]