Prism

Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.

Correct result:

S =  203.84 cm²
V =  139.2 cm³

Solution:

$$\begin{gathered} v=10 \\ a=5.8 \\ b=3 \\ w=2.4 \\ o=2\cdot (a+b)=2\cdot (5.8+3)={\displaystyle \frac{88}{5}}=17.6 \\ {S}_1=a\cdot w=5.8\cdot 2.4={\displaystyle \frac{348}{25}}=13.92 \\ S=2\cdot S_1+o\cdot v=2\cdot 13.92+17.6\cdot 10={\displaystyle \frac{5096}{25}}={\displaystyle \frac{5096}{25}}{\text{cm}}^2=203.84{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot v=13.92\cdot 10={\displaystyle \frac{696}{5}}={\displaystyle \frac{696}{5}}{\text{cm}}^3=139.2{\text{cm}}^3$

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