Question

o piramida patrulatera regulata are apotema 13 cm si muchia laterala de radical din 194 cm.calculati aria laterala si volumu piramidei

Answer 1

ap=13cm
m=√194cm
Al=?
V=?
Al=Pbap/2
Pb= 4l

Din DESEN reiese:
VM=ap = 13cm
VC= m = 194cm 
CM= BC/2
BC= latura bazei = L
==>CM= L /2
Unghiul M= 90* === > Conform. T lui Pitagora :
 VC^2 = VM^2 + CM^2
 m^2 = ap^2 + CM^2
CM^2= m^2-ap^2
CM^2 = 194 - 169
CM^2= 25
CM=√25
CM= 5 cm

CM= L/2
==> L= 2CM
L= 10 (cm)
Pb=4L
Pb=40cm
Al= Pbap/2
Al= 40 x 13/2
Al= 20x13
Al= 260 cm2
V= Abxh/3
Ab= L^2
Ab= 10cm^2
Ab= 100 cm2

Conform Desenului:
VO=h
VM= ap = 13 cm
OM = L/2 = 5 cm
Unghiul O are 90* ===> Conform T.lui Pitagora : 
VM^2 = VO^2+ OM^2
ap^2 = h^2 + 5^2
h^2= ap^2 - 5^2
h^2 = 13^2 - 5^2
h^2 = 169-25
h^2 =144
h= √144
h=12 cm
V= Abxh/3
V=100x12/3
V= 100x4
V= 400 cm3