The total surface area of the given prism is 152 square centimeters.
Step-by-step explanation:
The total surface area is given by:
![A_{T} = 2A_{t} + 2A_{r_{l}} + A_{r_{b}}](/tpl/images/1210/7185/98b33.png)
Where:
: is the area of the triangle of the prism (it has 2 triangles)
: is the area of the lateral rectangle of the prism (it has 2)
: is the area of the rectangle base of the prism (it has 1)
The area of the triangle is:
![A_{t} = \frac{bh}{2}](/tpl/images/1210/7185/e91ea.png)
Where:
b: is the triangle base = 6 cm
h: is the traingle height = 4 cm
![A_{t} = \frac{bh}{2} = \frac{6 cm*4 cm}{2} = 12 cm^{2}](/tpl/images/1210/7185/a5026.png)
The area of the lateral rectangle of the prism is:
![A_{r_{l}} = x*y = 8 cm*5 cm = 40 cm^{2}](/tpl/images/1210/7185/94fb2.png)
Now, the area of the rectangle base is:
![A_{r_{b}} = x*b = 8 cm*6 cm = 48 cm^{2}](/tpl/images/1210/7185/9647b.png)
Finally, the total surface area is:
![A_{T} = 2A_{t} + 2A_{r_{l}} + A_{r_{b}} = 2*12 + 2*40 + 48 = 152 cm^{2}](/tpl/images/1210/7185/d860c.png)
Therefore, the total surface area of the given prism is 152 square centimeters.
I hope it helps you!