O piramida patrulatera are latura bazei de 3√2 cm si muchia laterala de 5 cm. De aflat aria laterala ,aria totala, volumul.
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Notam VABCD piramida
AB=BC=CD=AD=3√2 cm
AC=√[(3√2)²+(3√2)²]=√(18+18)=√36=6 cm
VO inaltimea piramidei
OC=AC/2=3 cm
VO=√(5²+3²)=√(25-9)=√16=4 cm
ducem VM apotema piramidei adica VM_I_BC
OM=3√2/2
VM=√[(3√2/2)²+4²]=√(9*2/4+16)=√82 cm
Al=P*ap/2=4*3√2*√82/2=12√41 cm²
At=Al+Abaza=12√41 +(3√2)²=12√41 +18=6(2√41+3) cm²
V=Abaza *h/3=(3√2)²*4/3=18*4/3=24 cm³
AB=BC=CD=AD=3√2 cm
AC=√[(3√2)²+(3√2)²]=√(18+18)=√36=6 cm
VO inaltimea piramidei
OC=AC/2=3 cm
VO=√(5²+3²)=√(25-9)=√16=4 cm
ducem VM apotema piramidei adica VM_I_BC
OM=3√2/2
VM=√[(3√2/2)²+4²]=√(9*2/4+16)=√82 cm
Al=P*ap/2=4*3√2*√82/2=12√41 cm²
At=Al+Abaza=12√41 +(3√2)²=12√41 +18=6(2√41+3) cm²
V=Abaza *h/3=(3√2)²*4/3=18*4/3=24 cm³
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