Question

i need help on a question

Answer 1

Answer:

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

Step-by-step explanation:

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

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

Then, for the area of the base:

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

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

$\begin{gathered} A=\frac{1}{2}\cdot\text{base}\cdot\text{height} \\ A=\frac{1}{2}\cdot4\cdot2\sqrt[]{3} \\ A=4\sqrt[]{3} \end{gathered}$

So, for the total area:

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