# Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.

Result

S =  570 cm2

#### Solution:

$a = 7.5 \ \\ u = 12.5 \ \\ V = 0.9 \cdot \ 10^3 = 900 \ \\ b = \sqrt{ u^2-a^2 } = \sqrt{ 12.5^2-7.5^2 } = 10 \ \\ c = V/ (a \cdot \ b) = 900/ (7.5 \cdot \ 10) = 12 \ \\ S = 2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c) = 2 \cdot \ (7.5 \cdot \ 10+10 \cdot \ 12+7.5 \cdot \ 12) = 570 = 570 \ cm^2$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Do you want to convert length units? Do you know the volume and unit volume, and want to convert volume units? Pythagorean theorem is the base for the right triangle calculator.