Question

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find the surface area of this triangular prism. be sure to include

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A = \frac{1}{2}bh\). Here, \(b = 12\) cm and \(h = 16\) cm.
\(A_{triangle}=\frac{1}{2}\times12\times16 = 96\) \(cm^{2}\). Since there are 2 triangular bases, \(2\times A_{triangle}=2\times96 = 192\) \(cm^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with sides \(12\) cm and \(19\) cm: \(A_{1}=12\times19 = 228\) \(cm^{2}\)
• For the face with sides \(16\) cm and \(19\) cm: \(A_{2}=16\times19 = 304\) \(cm^{2}\)
• For the face with sides \(20\) cm and \(19\) cm: \(A_{3}=20\times19 = 380\) \(cm^{2}\)

The sum of the areas of the rectangular faces is \(A_{rectangles}=228 + 304+380=912\) \(cm^{2}\)

Step3: Calculate the total surface area

The total surface area \(A\) of the triangular prism is the sum of the areas of the triangular bases and the rectangular faces.
\(A=192 + 912\)

Answer:

\(1104\) \(cm^{2}\)