a triangular pyramid is shown below. which diagram is a net for this pyramid? what is the surface area of…

Answer:

The net on the left is the correct net for the triangular - pyramid. The surface area is 55.2 square centimeters.

Explanation:

Step1: Identify the base and lateral triangles

The base is an equilateral triangle with side length 6 cm. The lateral triangles have two sides of length 4 cm and 6 cm and height 5.2 cm.

Step2: Calculate the area of the base

The area of an equilateral triangle with side length (a = 6) cm is (A_{base}=\frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{3}}{4}\times6^{2}=\frac{\sqrt{3}}{4}\times36 = 9\sqrt{3}\approx15.6) square cm.

Step3: Calculate the area of one lateral triangle

The area of a triangle with base (b = 6) cm and height (h = 5.2) cm is (A_{lateral}=\frac{1}{2}\times b\times h=\frac{1}{2}\times6\times5.2 = 15.6) square cm.

Step4: Calculate the total surface area

Since there are 3 lateral triangles and 1 base, (A = A_{base}+3A_{lateral}). Substituting the values, (A=15.6 + 3\times15.6=15.6+46.8 = 55.2) square cm.