Triangular prism

Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm.

Correct answer:

S =  386.25 cm²

Step-by-step explanation:

$$\begin{gathered} a=7.5\text{cm} \\ v=6.5\text{cm} \\ h=15\text{cm} \\ {S}_1=\frac{a\cdot v}{2}=\frac{7.5\cdot 6.5}{2}=\frac{195}{8}=24.375{\text{cm}}^2 \\ o=3\cdot a=3\cdot 7.5=\frac{45}{2}=22.5\text{cm} \\ S=2\cdot S_1+o\cdot h=2\cdot \frac{195}{8}+\frac{45}{2}\cdot 15=\frac{1545}{4}{\text{cm}}^2=386.25{\text{cm}}^2 \end{gathered}$$

Try another example