Answer:
The surface area of the prism is [tex]1656 m^2[/tex].
Step-by-step explanation:
In order to obtain the surface area we need to find the areas of all the sides. Then, we have two triangles and three rectangles.
Let us find the area of the triangles and denote it by [tex]A_1[/tex]. Notice that both triangles are equal. We know that the area of a triangle is
[tex]A_t = bh/2[/tex]
where [tex]b[/tex] stands for the length of the base, and [tex]h[/tex] stands for the length of the height. From the figure we know that [tex]b=18m[/tex] and [tex]h=12m[/tex]. Hence, the area of the triangle is
[tex]A_t = bh/2=12\cdot 18/2=108 m^2.[/tex]
To obtain the area of both sides we only need to multiply [tex]A_t[/tex] by two:
[tex]A_1=2A_t=216 m^2.[/tex]
Let us find now the area of the bottom rectangle and denote by [tex]A_2[/tex]. The area of the rectangle is [tex]A_r = bh[/tex], where [tex]b[/tex] stands for the length of the base, and [tex]h[/tex] stands for the length of the height. From the figure we know [tex]h=18m[/tex] and [tex]b=30m[/tex]. So,
[tex]A_2=30\cdot 18 = 540m^2[/tex].
For the other two rectangle notice that they have the same dimensions: the length of the base is 30m and the length of the height is 15. So, the area of one of them is
[tex]A_3=30\cdot 15 = 450m^2[/tex].
Finally, the surface area is the result of adding all the areas:
[tex]A=A_1+A_2+2A_3 = 216 m^2 + 540 m^2 + 2\cdot 450 m^2 = 1656 m^2.[/tex]
