Question

Explain how you calculated the lateral surface zarea of the triangular prism. How could you use this information to help you calculate the total surface area of the triangular prism?

Answer 1

Calculating the lateral area of a triangular prism is equivalent to calculating the area of a rectangle.

`A=b\cdot h`

For this case the sides of the lateral area would be 14 and 12.

`A=12\cdot14=168`

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

`A_T=A_l+A_t`

Where

AT = Total area

Al = Lateral area

At = Area of the front triangle

`A_T=3A_l+2A_t`

The area of the triangle can be calculated as follows

`\begin{gathered} A_t=(1)/(2)\cdot b\cdot h \\ A_t=(1)/(2)\cdot12\cdot5 \\ A_t=(1)/(2)60 \\ A_t=30 \end{gathered}`

The total area would be

`\begin{gathered} A_T=3\cdot168+2\cdot30 \\ A_T=564 \end{gathered}`