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