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

Explanation:

Step1: Analyze the base triangle

The base is a right - angled triangle with legs of length 11 mm and 9.5 mm. The area of the base triangle $A_{base}=\frac{1}{2}\times11\times9.5=\frac{104.5}{2}=52.25$ $mm^{2}$.

Step2: Analyze the three lateral faces

1. For the first lateral face with base 11 mm and height 20 mm, its area $A_1=\frac{1}{2}\times11\times20 = 110$ $mm^{2}$.
2. For the second lateral face with base 9.5 mm and height 20 mm, its area $A_2=\frac{1}{2}\times9.5\times20=95$ $mm^{2}$.
3. For the third lateral face with base $\sqrt{11^{2}+9.5^{2}}=\sqrt{121 + 90.25}=\sqrt{211.25}\approx14.53$ mm and height 20 mm, its area $A_3=\frac{1}{2}\times\sqrt{11^{2}+9.5^{2}}\times20=\frac{1}{2}\times14.53\times20 = 145.3$ $mm^{2}$.

Step3: Calculate the surface area

The surface area $A = A_{base}+A_1 + A_2+A_3=52.25+110 + 95+145.3=402.55$ $mm^{2}$.

Answer:

402.55