areaThe Lateral area of a Triangular prism is the area of the sides
The sides of the prism are two Rectangles.
We need to calculate the Hypotenues side of right angle triangle
[tex]\begin{gathered} \text{hyp}^2=\text{adj}^2+\text{opp}^2 \\ \text{hyp}^2=12^2+3^2 \\ =144+9 \\ =153 \\ \text{hyp}=\sqrt[]{153}=3\sqrt[]{17} \end{gathered}[/tex]
The lateral Area is given as
Area the side excluding the area of the base
[tex]\begin{gathered} \text{atrea of rectangle =l}\times b \\ =(8\times3\sqrt[]{17})+(8\times12) \\ =24\sqrt[]{17}+96 \\ =194.95\operatorname{cm}^2 \end{gathered}[/tex]
The surface area of the prism is the area of all the surface
Area of 2Rectangles+Area of 2 Triangles +Area of the Base rectangle
The area of the two rectangles is given as LxB
[tex]\begin{gathered} \text{area of rectangle =(8}\times3\sqrt[]{17})+(8\times12) \\ =194.95\operatorname{cm}^2 \end{gathered}[/tex]
The are of the Two Triangles is given as
[tex]\begin{gathered} \frac{1}{2}ab\sin \emptyset \\ \text{where a=12,b=3,and }\emptyset=90^0 \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{2}\times3\times12\times\sin 90^0 \\ =3\times6=18cm^2 \\ \text{where sin90=1} \\ \text{the area of the two triangle is } \\ 18\times2=36\operatorname{cm}^2 \end{gathered}[/tex]
