Question

find the surface area of the triangular prism shown below.

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 14$ and $h = 8$, so $A_{base}=\frac{1}{2}\times14\times8= 56$. Since there are 2 triangular bases, the total area of the bases is $2\times56 = 112$.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
For the first rectangular face with dimensions 10 and 12: $A_1=10\times12 = 120$.
For the second rectangular face with dimensions 10 and 14: $A_2=10\times14 = 140$.
For the third rectangular face with dimensions 10 and 12: $A_3=10\times12 = 120$.
The total area of the rectangular faces is $A_{rect}=120 + 140+120=380$.

Step3: Calculate total surface - area

The surface - area of the triangular prism $A = A_{base}+A_{rect}$. So $A=112 + 380=492$.

Answer:

492