Question

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Answer 1

`\text{ T.A=28}\sqrt[]{3}\approx48.5`

Explanation:

The total area of a regular triangular pyramid is represented by the following expression:

`\begin{gathered} \text{ T.A=A+}(1)/(2)\cdot p\cdot s \\ \text{where,} \\ A=\text{area of base} \\ p=\text{perimeter of base} \\ s=\text{slant height} \end{gathered}`

Then, for the area of the base:

As a first step, calculate the height of the triangles with the Pythagorean theorem:

`\begin{gathered} h=\sqrt[]{4^2-2^2} \\ h=\sqrt[]{12}=2\sqrt[]{3} \end{gathered}`

`\begin{gathered} A=(1)/(2)\cdot\text{base}\cdot\text{height} \\ A=(1)/(2)\cdot4\cdot2\sqrt[]{3} \\ A=4\sqrt[]{3} \end{gathered}`

So, for the total area:

`\begin{gathered} \text{ T.A=4}\sqrt[]{3}+(1)/(2)\cdot12\cdot4\sqrt[]{3} \\ \text{ T.A=28}\sqrt[]{3}\approx48.5 \end{gathered}`