Explicație pas cu pas:
a) lungimea apotemei bazei ABCD:
[tex] = \sqrt{ {20}^{2} - {16}^{2}} = \sqrt{144} = 12 \: cm[/tex]
b) lungimea muchiei bazei ABCD:
[tex]= 2 \times apotema_{bazei} = 2 \times 12 = 24 \: cm[/tex]
c) volumul piramidei VABCD:
[tex]Aria_{bazei} = A_{b} = {l}^{2} = {24}^{2} = 576 \: {cm}^{2}[/tex]
[tex]V = \frac{A(b) \times h}{3} = \frac{ {l}^{2} \times h }{3} = \frac{ {24}^{2} \times 16 }{3} = 3072 \: cm^{3}[/tex]
d) aria totală a piramidei VABCD:
[tex]Aria_{laterala} =A_{l} = \frac{perimetrul_{bazei} \times apotema_{piramidei}}{2}= \frac{4 \times l \times a_{p}}{2} = \frac{4 \times 24 \times 20}{2} = 960 \: cm^{2}[/tex]
[tex]A_{t} = A_{l} + A_{b} = 960 + 576 = 1536 \: {cm}^{2}[/tex]
