Calculating the lateral area of a triangular prism is equivalent to calculating the area of a rectangle.
[tex]A=b\cdot h[/tex]
For this case the sides of the lateral area would be 14 and 12.
[tex]A=12\cdot14=168[/tex]
The lateral area of a prism triangle is repeated three times because we have three faces of the same proportions.
To calculate the total area the formula would be as follows
[tex]A_T=A_l+A_t[/tex]
Where
AT = Total area
Al = Lateral area
At = Area of the front triangle
[tex]A_T=3A_l+2A_t[/tex]
The area of the triangle can be calculated as follows
[tex]\begin{gathered} A_t=\frac{1}{2}\cdot b\cdot h \\ A_t=\frac{1}{2}\cdot12\cdot5 \\ A_t=\frac{1}{2}60 \\ A_t=30 \end{gathered}[/tex]
The total area would be
[tex]\begin{gathered} A_T=3\cdot168+2\cdot30 \\ A_T=564 \end{gathered}[/tex]
