Question

what is the surface area of this triangular pyramid? 20 cm 13 cm 20 cm 20 cm 17.3 cm square centimeters

Explanation:

Step1: Find area of base triangle

The base is an equilateral triangle with side length $a = 20$ cm. The area of an equilateral triangle is $A_{base}=\frac{\sqrt{3}}{4}a^{2}$. So $A_{base}=\frac{\sqrt{3}}{4}\times20^{2}=\frac{\sqrt{3}}{4}\times400 = 100\sqrt{3}\approx173$ $cm^{2}$.

Step2: Find area of one lateral - face triangle

The lateral - face triangles have base $b = 20$ cm and height $h = 13$ cm. The area of a triangle is $A=\frac{1}{2}bh$. So the area of one lateral - face triangle is $A_{lateral}=\frac{1}{2}\times20\times13 = 130$ $cm^{2}$.

Step3: Calculate total surface area

A triangular pyramid has 1 base and 3 lateral faces. The total surface area $A_{total}=A_{base}+3A_{lateral}$. Substitute the values: $A_{total}=173 + 3\times130=173+390 = 563$ $cm^{2}$.

Answer:

563