To find the surface area of a prism, we must find the area of each side and add them up.
Let's first find the area of the triangular base.
The area of a triangle is [tex] \dfrac{1}{2} bh[/tex]
Where b is the base length and h is the height.
The base length of the triangle is 10.5. The height is 10.
[tex]A_B= \dfrac{1}{2}bh= \dfrac{1}{2} \times 10 \times 10.5=52.5[/tex]
The triangular base has an area of 52.5 cm².
The triangular top must also have the same area. Thus, it also has an area of 52.5 cm².
Now we to find the length of the 3 rectangles on the side of the prism.
The formula for the area of a rectangle is [tex]A=wl[/tex]
where [tex]w[/tex] is the width and [tex]l[/tex] is the length.
All rectangles have a width of 8. They all have different lengths. If we find the area of all the rectangles, we have the following:
[tex]A_1=8 \times 10.5 = 84[/tex]
[tex]A_2=8 \times 10 = 80[/tex]
[tex]A_3=8 \times 14.5=116[/tex]
Now, add up ALL the areas we found. We'll have our surface area once we do this.
[tex]52.5+52.5+84+80+116=385[/tex]
The surface area is 385 cm². Hope this helps! :)
