which diagram is a net for this prism? what is the surface area of the triangular prism? square centimeters

Answer:

1280

Explanation:

Step1: Calculate area of triangular faces

The triangular faces have base $b = 16$ cm and height $h=12$ cm. Area of a triangle $A_{triangle}=\frac{1}{2}bh$. So $A_{triangle}=\frac{1}{2}\times16\times12 = 96$ square - cm. There are 2 triangular faces, so total area of triangular faces $A_{t - total}=2\times96 = 192$ square - cm.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions $16$ cm and $20$ cm. Area $A_{1}=16\times20 = 320$ square - cm.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions $12$ cm and $20$ cm. Area $A_{2}=12\times20 = 240$ square - cm.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $20$ cm and $\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20$ cm. Area $A_{3}=20\times20 = 400$ square - cm.

Step5: Calculate total surface area

Total surface area $A = A_{t - total}+A_{1}+A_{2}+A_{3}=192 + 320+240 + 400=1280$ square - cm.