Question

2.) find the surface area of the triangular prism below. show all work! 10 in 8 in 10 in 14 in 12 in

Explanation:

Step1: Calculate area of triangular faces

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

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 10 in (width) and 14 in (length). Its area $A_{rect1}=10\times14 = 140$ square inches.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 10 in (width) and 14 in (length). Its area $A_{rect2}=10\times14 = 140$ square inches.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 12 in (width) and 14 in (length). Its area $A_{rect3}=12\times14 = 168$ square inches.

Step5: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of the triangular faces and the rectangular faces. So $A=96 + 140+140 + 168=544$ square inches.

Answer:

544 square inches