Question

what is the surface area of this triangular prism? 10 in. 8 in. 10 in. 12 in. 15 in. square inches

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 12$ in and $h=8$ in. So, $A_{triangle}=\frac{1}{2}\times12\times8=48$ square - inches. Since there are 2 triangular faces, the total area of triangular faces is $2\times48 = 96$ square - inches.

Step2: Calculate area of first rectangular face

The dimensions of the first rectangular face are $10$ in (height) and $15$ in (length). So, $A_{rect1}=10\times15 = 150$ square - inches.

Step3: Calculate area of second rectangular face

The dimensions of the second rectangular face are $10$ in (height) and $10$ in (length). So, $A_{rect2}=10\times10 = 100$ square - inches.

Step4: Calculate area of third rectangular face

The dimensions of the third rectangular face are $10$ in (height) and $12$ in (length). So, $A_{rect3}=10\times12 = 120$ square - inches.

Step5: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of all the faces. $A=96 + 150+100 + 120=466$ square - inches.

Answer:

466