find the surface area of this regular triangular pyramid. sa = cm²

Question

Accepted Answer

# Explanation:
## Step1: Find the area of the base
The base is an equilateral triangle with side length $a = 10$ cm. The area of an equilateral triangle is $A_{base}=\frac{\sqrt{3}}{4}a^{2}$.
$$
\begin{align*}
A_{base}&=\frac{\sqrt{3}}{4}\times10^{2}\
&=\frac{\sqrt{3}}{4}\times100\
& = 25\sqrt{3}\text{ cm}^2\
&\approx25\times1.732 = 43.3\text{ cm}^2
\end{align*}
$$
## Step2: Find the area of one lateral face
The lateral face is a triangle with base $b = 10$ cm and height $h = 8.66$ cm. The area of a triangle is $A_{lateral}=\frac{1}{2}bh$.
$$
\begin{align*}
A_{lateral}&=\frac{1}{2}\times10\times8.66\
&= 43.3\text{ cm}^2
\end{align*}
$$
## Step3: Calculate the total surface area
A regular triangular pyramid has $3$ lateral faces and $1$ base.
$$
\begin{align*}
SA&=A_{base}+3A_{lateral}\
&=43.3+3\times43.3\
&=43.3\times(1 + 3)\
&=173.2\text{ cm}^2
\end{align*}
$$

# Answer:
$173.2$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find the area of the base

Step2: Find the area of one lateral face

Step3: Calculate the total surface area

Answer: