Answer:
The surface area of the triangular prism is [tex]A=122\:in^2[/tex].
Step-by-step explanation:
The surface area of any prism is the total area of all its sides and faces. A triangular prism has three rectangular sides and two triangular faces.
An equilateral triangle is a triangle with all three sides of equal length.
To find the surface area, the area of each face is calculated and then add these areas together.
The formula [tex]A=\frac{1}{2} bh[/tex] is used to find the area of the triangular faces, where A = area, b = base, and h = height.
The formula [tex]A=lw[/tex] is used to find the area of the three rectangular side faces, where A = area, l = length, and w = width.
The surface area of the triangular faces is:
[tex]A=\frac{1}{2} (4)(3.5)+\frac{1}{2} (4)(3.5)\\A=2\cdot \:4\cdot \:3.5\cdot \frac{1}{2}\\A=1\cdot \:4\cdot \:3.5\\A=14\:in^2[/tex]
The surface area of the three rectangular side faces is:
[tex]A=4\cdot9+4\cdot9+4\cdot9=108\:in^2[/tex]
The surface area of the triangular prism is [tex]A=14+108=122\:in^2[/tex].
