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

Explanation:

Step1: Recall net - concept

A net of a triangular pyramid is a 2 - D shape that can be folded to form the 3 - D triangular pyramid. We need to match the side - lengths and right - angle markings.

Step2: Analyze the first net

The first net has the correct combination of side - lengths and right - angle markings that match the given triangular pyramid. The second net has an incorrect arrangement of the triangles and side - lengths.

Step3: Calculate surface area

The triangular pyramid has 4 triangular faces. Let's consider the base triangle with base (b = 20) mm and height (h_1=17.3) mm. The area of the base (A_{base}=\frac{1}{2}\times b\times h_1=\frac{1}{2}\times20\times17.3 = 173) (mm^{2}). There are 3 triangular faces with base (b = 20) mm and height (h_2 = 16) mm. The area of each of these faces (A_{lateral}=\frac{1}{2}\times b\times h_2=\frac{1}{2}\times20\times16=160) (mm^{2}). The total surface area (A = A_{base}+3\times A_{lateral}). Substitute the values: (A=173 + 3\times160=173+480 = 653) (mm^{2}).

Answer:

The net is the first diagram. The surface area of the triangular pyramid is (653) (mm^{2}).