Question

find the surface area of the right triangular prism shown below.

Explanation:

Step1: Calculate area of triangular bases

The base is a right - triangle with legs 3 and 4. Area of a triangle $A_{base}=\frac{1}{2}\times3\times4 = 6$. Since there are 2 bases, the total area of the bases $A_{total - bases}=2\times6 = 12$.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
Face 1 with dimensions 3 and 11, area $A_1 = 3\times11=33$.
Face 2 with dimensions 4 and 11, area $A_2 = 4\times11 = 44$.
Face 3 with dimensions 5 and 11, area $A_3=5\times11 = 55$.
The total area of the rectangular faces $A_{total - rectangles}=33 + 44+55=132$.

Step3: Calculate total surface area

The surface area of the prism $A = A_{total - bases}+A_{total - rectangles}=12 + 132=144$.

Answer:

144