Răspuns :
LA PIRAMIDA : Ab=l la puterea a2a (pentru baza patrat); l la puterea a2a rad din 3/4 pentru baza triunghi echilateral. Al=Pb(perimetrul bazei)*apotema/2 At=Al=Ab V=Ab*h/3 CUB:Ab=l(latura) la puterea a2a; Al=4l la a2a, At=6l la a doua (doar l e la a 2a),V=L la puterea a3a; diagonala=l rad din 3. PARALELIPIPED:Ab=L*l; Al=Pb*h; At=2Ab=Al;V=Ab*h Dreptunghi:A=L*l (lungime * latime), P=2(L+l) sau aduni laturile pur si simplu. PATRAT:P=4*l;A=l la puterea a 2a.
Prisma :
Alat = Pbazei *h
Atot = Alat + 2Abazei
V = Abazei*h
Cub :
Alat = [tex]4l^{2} [/tex]
Atot = [tex] 6l^{2} [/tex]
V = [tex] l^{3} [/tex]
d = [tex] l\sqrt{3} [/tex]
Paralelipiped ( a- lungimea bazei; b - latimea bazei; c- inaltimea )
Alat= 2c(a+b)
Atot= 2(ab+ac+bc)
V=a*b*c
d=[tex] \sqrt{a^{2}+ b^{2}+ c^{2} } [/tex]
Piramida
Alat=[tex] \frac{Pbazei*a.pir}{2} [/tex]
Atot=Alat+Abazei
V=[tex] \frac{Abazei*h}{3} [/tex]
Tetraedrul regulat
Alat=3*[tex] \frac{ l^{2} \sqrt{3} }{4} [/tex]
Atot= [tex] l^{2} \sqrt{3} [/tex]
V= [tex] \frac{l^{3} \sqrt{2} }{12} [/tex]
h= [tex] \frac{ l\sqrt{6} }{3} [/tex]
Patrat
A=[tex] l^{2} [/tex]
d=[tex] l\sqrt{2} [/tex]
Dreptunghi
A= L*l
Triunghi echilateral
h=[tex] \frac{ l\sqrt{3}}{2} [/tex]
A=[tex] \frac{ l^{2} \sqrt{3} }{4} [/tex]
Cerc
Lcerc = 2[tex] \pi [/tex]r
Adisc = [tex] \pi r^{2} [/tex]
Alat = Pbazei *h
Atot = Alat + 2Abazei
V = Abazei*h
Cub :
Alat = [tex]4l^{2} [/tex]
Atot = [tex] 6l^{2} [/tex]
V = [tex] l^{3} [/tex]
d = [tex] l\sqrt{3} [/tex]
Paralelipiped ( a- lungimea bazei; b - latimea bazei; c- inaltimea )
Alat= 2c(a+b)
Atot= 2(ab+ac+bc)
V=a*b*c
d=[tex] \sqrt{a^{2}+ b^{2}+ c^{2} } [/tex]
Piramida
Alat=[tex] \frac{Pbazei*a.pir}{2} [/tex]
Atot=Alat+Abazei
V=[tex] \frac{Abazei*h}{3} [/tex]
Tetraedrul regulat
Alat=3*[tex] \frac{ l^{2} \sqrt{3} }{4} [/tex]
Atot= [tex] l^{2} \sqrt{3} [/tex]
V= [tex] \frac{l^{3} \sqrt{2} }{12} [/tex]
h= [tex] \frac{ l\sqrt{6} }{3} [/tex]
Patrat
A=[tex] l^{2} [/tex]
d=[tex] l\sqrt{2} [/tex]
Dreptunghi
A= L*l
Triunghi echilateral
h=[tex] \frac{ l\sqrt{3}}{2} [/tex]
A=[tex] \frac{ l^{2} \sqrt{3} }{4} [/tex]
Cerc
Lcerc = 2[tex] \pi [/tex]r
Adisc = [tex] \pi r^{2} [/tex]