Respuesta :
We have been given an image of a triangular prism. We are asked to find the total surface area of the the prism.
The total surface area of the prism wold be sum of areas of all faces.
First of all, we will find the area of base and other two rectangles on sides.
[tex]\text{Area of base}=(5+9)\times 20[/tex]
[tex]\text{Area of base}=14\times 20=280[/tex]
[tex]\text{Area of other two rectangular faces}=15\times 20+13\times 20[/tex]
[tex]\text{Area of other two rectangular faces}=300+260[/tex]
[tex]\text{Area of other two rectangular faces}=560[/tex]
Now we need to find the area of two triangular faces.
[tex]\text{Area of other two triangular faces}=2\times \frac{1}{2}\times (5+9)\times 12[/tex]
[tex]\text{Area of other two triangular faces}=14\times 12[/tex]
[tex]\text{Area of other two triangular faces}=168[/tex]
[tex]\text{Total surface area}=280+560+168[/tex]
[tex]\text{Total surface area}=1008[/tex]
Therefore, the total surface area of the prism is 1008 square cm.
The total surface area of the triangular prism can be calculate by computing the area of all the shapes present in prism.
The total area of the triangular prism is [tex]1008\:\rm cm^2[/tex].
Given:
The prism base is [tex]=15\:\rm cm\times 9\:\rm cm[/tex]
The middle line is [tex]12\:\rm cm[/tex].
The base of prism is rectangular so calculate the area of base.
[tex]A_1=(5+9)\times 20\\A_1=14\times 20\\A_1=280[/tex]
In the given figure there are two rectangular faces. Calculate the area of two rectangular faces.
[tex]A_2=15\times 20+13\times 20\\A_2=300+260\\A_2=560\:\rm cm^2[/tex]
In the given figure there are two triangular faces. Calculate the area of two rectangular faces.
[tex]A_3=2\times \dfrac{1}{2}\times (5+9)\times 12\\A_3=14\times 12\\A_3=168[/tex]
Calculate the total area of the triangular prism.
[tex]A=A_1+A_2+A_3\\A=280+560+168\\A=1008\:\rm cm^2[/tex]
Thus, the total area of the triangular prism is [tex]1008\:\rm cm^2[/tex].
Learn more about surface area here:
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