Task 510
Task 510: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Two right triangles share a side as follows: asy pair pA, pB, pC, pD, pE; pA = (0, 0); pB = pA + 6 dir(0); pC = pA + 10 dir(90); pD = pB + 6 dir(90); pE = (6 pA + 10 pD) / 16; draw(pA--pB--pC--pA)…
The task
Two right triangles share a side as follows: [asy] pair pA, pB, pC, pD, pE; pA = (0, 0); pB = pA + 6 * dir(0); pC = pA + 10 * dir(90); pD = pB + 6 * dir(90); pE = (6 * pA + 10 * pD) / 16; draw(pA--pB--pC--pA); draw(pA--pB--pD--pA); label("$A$", pA, SW); label("$B$", pB, SE); label("$C$", pC, NW); label("$D$", pD, NE); label("$E$", pE, 3 * N); label("$6$", pA--pB, S); label("$10$", pA--pC, W); label("$6$", pB--pD, E); draw(rightanglemark(pB,pA,pC,12)); draw(rightanglemark(pD,pB,pA,12)); [/asy] What is the area of $\triangle ACE$?