step 1
Find out the lateral surface area of the triangular prism
The lateral area is the area of the three rectangular faces
[tex]LA=P*H[/tex]
where
P is the perimeter of the triangular face
H is the height of the prism
H=9.5 mm
[tex]\begin{gathered} P=10.5+7.5+11 \\ P=29\text{ mm} \end{gathered}[/tex]
substitute
[tex]\begin{gathered} LA=29*9.5 \\ LA=275.5\text{ mm}^2 \end{gathered}[/tex]
The lateral area is 275.5 square millimeters
step 2
Find out the surface total area
The surface area is equal to the lateral area plus two times the area of the triangular face
[tex]SA=LA+2B[/tex]
where
B is the area of the triangular face
[tex]B=\frac{1}{2}*b*h[/tex]
where
b=10.5 mm
h=6 mm
substitute
[tex]\begin{gathered} B=\frac{1}{2}*10.5*6 \\ B=31.5\text{ mm}^2 \end{gathered}[/tex]
substitute in the formula of surface area
[tex]\begin{gathered} SA=275.5+2*31.5 \\ SA=338.5\text{ mm}^2 \end{gathered}[/tex]
The surface area is 338.5 square millimeters
