what is the surface area of this triangular pyramid? square centimeters

Explanation:

Step1: Calculate base - area

The base is an equilateral triangle with side length $a = 13$ cm. The area of an equilateral triangle $A_{base}=\frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{3}}{4}\times13^{2}=\frac{169\sqrt{3}}{4}\approx73.6$ $cm^{2}$.

Step2: Calculate area of one lateral - face

The lateral - faces are isosceles triangles with base $b = 13$ cm and height $h = 17$ cm. The area of one lateral - face $A_{lateral}=\frac{1}{2}\times b\times h=\frac{1}{2}\times13\times17 = 110.5$ $cm^{2}$.

Step3: Calculate total surface area

A triangular pyramid has 1 base and 3 lateral - faces. $A = A_{base}+3A_{lateral}=\frac{169\sqrt{3}}{4}+3\times110.5\approx73.6 + 331.5=405.1$ $cm^{2}$.

Answer:

$405.1$