Question

a triangular prism is shown below. which diagram is a net for this prism? what is the surface area of the triangular prism? square feet

Explanation:

Step1: Calculate area of triangular faces

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 24$ ft and $h=16$ ft. So, $A_{triangle}=\frac{1}{2}\times24\times16= 192$ square - feet. Since there are 2 triangular faces, the total area of triangular faces is $2\times192 = 384$ square - feet.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 8 ft and 24 ft. Using the formula for the area of a rectangle $A = lw$, we get $A_{rect1}=8\times24 = 192$ square - feet.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 8 ft and 20 ft. So, $A_{rect2}=8\times20 = 160$ square - feet.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 8 ft and 20 ft. So, $A_{rect3}=8\times20 = 160$ square - feet.

Step5: Calculate total surface area

The total surface area $A_{total}$ of the triangular prism is the sum of the areas of all the faces. $A_{total}=384 + 192+160 + 160=896$ square - feet.

Answer:

896