[{"data":1,"prerenderedAt":128},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Fgeometria\u002Fprisma-y-piramide?{}":3,"topics-with-content:geometria":113},{"course":4,"topic":12,"counts":17,"universities":22,"channels":35,"sampleQuestions":68,"sameName":112},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},3,"geometria","Geometría","Geom.","math","i-lucide-triangle",2,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},311,"prisma-y-piramide","Prisma y pirámide",10,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},23,118,86,1886,[23,31],{"universityId":11,"questions":24,"years":25},12,[26,27,28,29,30],2026,2025,2024,2023,2022,{"universityId":32,"questions":33,"years":34},1,11,[27,28,29,30],[36,39,41,44,47,49,52,55,58,60,62,64,66],{"name":37,"classes":38},"Alberto Cruz",27,{"name":40,"classes":18},"Academia Grupo Ciencias",{"name":42,"classes":43},"Academia ipluton",21,{"name":45,"classes":46},"Ciclo Uni-San Marcos",9,{"name":48,"classes":46},"Salón Sapiens",{"name":50,"classes":51},"Academias Aduni y César Vallejo",8,{"name":53,"classes":54},"Pamer Corporación Educativa",7,{"name":56,"classes":57},"CEPRE UNMSM",6,{"name":59,"classes":5},"Trilce Multimedia",{"name":61,"classes":11},"Academia Internet",{"name":63,"classes":32},"Academia_Pitagoras",{"name":65,"classes":32},"META VILLARREAL",{"name":67,"classes":32},"Saco Oliveros",[69,95],{"id":70,"courseId":5,"topicId":13,"pastExamId":71,"stem":72,"options":73,"correctKey":81,"explanation":89,"difficulty":90,"status":91,"source":92,"stats":93},1648,198,"En una pirámide regular $V-ABCD$, todas las aristas son congruentes. En $\\overline{AD}$ y $\\overline{CD}$ se ubican los puntos $E$ y $F$, respectivamente, tal que $\\overline{BE}$ interseca a $\\overline{AF}$ en el punto $G$. Si $DE=3u$ y las áreas de las regiones triangulares $AGE$ y $BFG$, son $\\dfrac{9}{5}u^{2}$ y $\\dfrac{54}{5}u^{2}$, respectivamente, entonces calcule el volumen (en $u^{3}$) del sólido limitado por la pirámide.",[74,77,80,83,86],{"key":75,"text":76},"A","$28\\sqrt{2}$",{"key":78,"text":79},"B","$30\\sqrt{2}$",{"key":81,"text":82},"C","$36\\sqrt{2}$",{"key":84,"text":85},"D","$40\\sqrt{2}$",{"key":87,"text":88},"E","$48\\sqrt{2}$","",5,"published","UNI 2026-1 · Matemática",{"attempts":94,"accuracy":94},0,{"id":96,"courseId":5,"topicId":13,"pastExamId":97,"stem":98,"options":99,"correctKey":87,"explanation":89,"difficulty":5,"status":91,"source":110,"stats":111},1832,201,"Un prisma triangular regular está circunscrito a una esfera de longitud de radio $r$. Determine el área total del prisma.",[100,102,104,106,108],{"key":75,"text":101},"$6\\sqrt{3}\\,r^2$",{"key":78,"text":103},"$10\\sqrt{3}\\,r^2$",{"key":81,"text":105},"$12\\sqrt{3}\\,r^2$",{"key":84,"text":107},"$15\\sqrt{3}\\,r^2$",{"key":87,"text":109},"$18\\sqrt{3}\\,r^2$","UNI 2026-2 · Matemática",{"attempts":94,"accuracy":94},[],[114,115,116,117,118,119,120,121,122,123,13,124,125,126,127],301,302,303,304,305,306,307,308,309,310,312,313,314,315,1791501527170]