Vertical prism

The base of the vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism

Correct answer:

S =  960 cm²
V =  900 cm³

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ c=13\text{cm} \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12\text{cm} \\ h=a+b+c=5+12+13=30\text{cm} \\ P=a\cdot b/2=5\cdot 12/2=30{\text{cm}}^2 \\ S=2\cdot P+a\cdot h+b\cdot h+c\cdot h=2\cdot 30+5\cdot 30+12\cdot 30+13\cdot 30=960{\text{cm}}^2 \end{gathered}$$

$V=P\cdot h=30\cdot 30=900{\text{cm}}^3$

Try another example