Prism

Calculate the surface area and volume of a prism with a body height h = 10 cm, and its base has the 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 answer:

S =  203.84 cm²
V =  139.2 cm³

Step-by-step explanation:

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

$V=S_1\cdot v=\frac{348}{25}\cdot v=13.92\cdot 10=139.2{\text{cm}}^3$

Try another example