Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces with base $b = 24$ ft and height $h=10$ ft, $A_{triangle}=\frac{1}{2}\times24\times10= 120$ ft². Since there are 2 triangular faces, the total area of triangular faces is $2\times120 = 240$ ft².

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions 14 ft (length) and 24 ft (width). Its area $A_{1}=14\times24 = 336$ ft².

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions 14 ft (length) and 10 ft (width). Its area $A_{2}=14\times10 = 140$ ft².

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 14 ft (length) and 26 ft (width). Its area $A_{3}=14\times26 = 364$ ft².

Step5: Calculate total surface area

The total surface - area $A = 240+336 + 140+364=1080$ ft².

Answer:

$1080$ ft²