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: Identify base - triangle area

The base is a right - triangle with legs 5 ft and 12 ft. Area of a triangle formula is $A=\frac{1}{2}bh$. So, $A_{triangle}=\frac{1}{2}\times5\times12 = 30$ square feet.

Step2: Identify rectangle areas

There are three rectangles. One with dimensions 15 ft and 5 ft, area $A_1 = 15\times5=75$ square feet; one with dimensions 15 ft and 12 ft, area $A_2 = 15\times12 = 180$ square feet; one with dimensions 15 ft and 13 ft, area $A_3=15\times13 = 195$ square feet.

Step3: Calculate surface area

The surface area $SA$ of the triangular prism is the sum of the areas of the two bases and the three rectangles. Since there are two bases, $SA = 2\times A_{triangle}+A_1 + A_2+A_3$. Substitute the values: $SA=2\times30 + 75+180 + 195=60+75+180+195 = 510$ square feet.

Answer:

510