Question

Piramida patrulaterà regulatà VABCD, cu vârful V, are aria totalà de 384 cm^3 si aria lateralá de 240 cm^2. Calculati:
a) aria bazei ABCD;
c) lungimea inaltimii piramidei;
b) lungimea apotemei piramidei:
d) volumul piramidei.

Answer 1

Răspuns:

a)a) aria bazei ABCD;

384-240=144cm²

b) lungimea apotemei piramidei

l bazei=√144=12cm

A lat=384=4×l×A/2=4×12×A/2=48/2A=24A

A=384/24=16cm

c) lungimea inaltimii piramidei;

h=√A²-(l/2)²=√16²-6²=√220≈15cm

d) volumul piramidei.

V=Abazei×h/3=144×15/3=144×5=720cm³