# Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.

Result

S =  524 cm2
V =  720 cm3

#### Solution:

$a = 12 \ cm \ \\ b = 7 \ cm \ \\ v = 6 \ cm \ \\ h = 10 \ cm \ \\ \ \\ S_{ 1 } = a \cdot \ v = 12 \cdot \ 6 = 72 \ cm^2 \ \\ S_{ 2 } = h \cdot \ (2 \cdot \ a+2 \cdot \ b) = 10 \cdot \ (2 \cdot \ 12+2 \cdot \ 7) = 380 \ cm^2 \ \\ \ \\ S = 2 \cdot \ S_{ 1 } + S_{ 2 } = 2 \cdot \ 72 + 380 = 524 = 524 \ cm^2$
$V = S_{ 1 } \cdot \ h = 72 \cdot \ 10 = 720 = 720 \ cm^3$

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