Answer:
[tex]240\ cm^2[/tex]
Step-by-step explanation:
Surface Area of Solids
It's the total area of the sides of a given solid. The given object is formed by two triangles and three rectangles. To compute the total surface area, we find each individual area as follows.
Area of a triangle
[tex]\displaystyle A_t=\frac{b.h}{2}[/tex]
We can see in the image the base and the height of the triangles are perpendicular as requested, so
[tex]\displaystyle A_t=\frac{6\times 8}{2}=24\ cm^2[/tex]
Since there are two triangles
[tex]2A_t=48\ cm^2[/tex]
Area of rectangles
The base of the solid is a rectangle with dimensions of 8 cm x 10 cm. The area is
[tex]A_1=8\times 10 = 80\ cm^2[/tex]
The left lateral surface is a rectangle with dimensions of 8 cm x 8 cm. The area is
[tex]A_2=8\times 8 = 64\ cm^2[/tex]
The right lateral surface is a rectangle with dimensions of 8 cm x 6 cm. The area is
[tex]A_3=8\times 6 = 48\ cm^2[/tex]
The total surface area is
[tex]\boxed{A=240\ cm^2}[/tex]
