Triangular prism

The triangular prism has a base in the shape of a right triangle, the legs of which are 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?

Correct answer:

V =  3600 cm³
S =  2160 cm²

Step-by-step explanation:

$$\begin{gathered} a=9\text{cm} \\ b=40\text{cm} \\ h=20\text{cm} \\ c=\sqrt{a^2+b^2}=\sqrt{9^2+40^2}=41\text{cm} \\ {S}_1=\frac{a\cdot b}{2}=\frac{9\cdot 40}{2}=180{\text{cm}}^2 \\ V=S_1\cdot h=180\cdot 20=3600{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} o=a+b+c=9+40+41=90\text{cm} \\ S=2\cdot S_1+o\cdot h=2\cdot 180+90\cdot 20=2160{\text{cm}}^2 \end{gathered}$$

Try another example