Question

Please help with this problem. need layers and total area

Answer 1

Given a triangular base pyramid with the following dimensions

`\begin{gathered} For\text{ the lateral sides} \\ h=12m \\ b=8m \\ \text{For the base} \\ h=6.9m \\ b=8m \end{gathered}`

To find the total surface area, TSA, of the triangular base pyramid, the formula is

`\text{TSA}=\text{base area}+(1)/(2)(Perimeter* slant\text{ height)}`

The base area of the triangular base pyramid is

`\text{Base area}=(1)/(2)bh=(1)/(2)*8*6.9=27.6m^2`

For the other part of the total surface area

`\begin{gathered} (1)/(2)(Perimeter* slant\text{ height)}=(1)/(2)((8+8+8)*12) \\ =(1)/(2)(24*12)=(1)/(2)*288=144m^2 \end{gathered}`

The total surface area of the triangular base pyramid is

`\text{TSA}=\text{base area}+(1)/(2)(Perimeter* slant\text{ height)}=27.6+144=171.6m^2`

Hence, the total surface area of the triangular base pyramid is 171.6m²

To find the lateral area of a triangular base pyramid, the formula is

`\begin{gathered} Lateral\text{ area}=(1)/(2)(Perimeter* slant\text{ height)} \\ =(1)/(2)((8+8+8)*12) \\ (1)/(2)(24*12)=(1)/(2)(24*12)=(1)/(2)(288)=144m^2 \\ Lateral\text{ area}=144m^2 \end{gathered}`

Hence, the lateral area of the triangular base pyramid is 144m²