1 Answer

Hemali · Answer 1 · 2023-02-27T03:43:10+0000

To calculate the area fo a triangular prism you have to calculate the are of each side of the prism ad add them.

The triangles are right triangles, their base is b=6in and their heigth is h=8in

The area of each one of them can be calculated as

Since there are 2 of them and are equal, you have to multiply it by 2, so the area of both triangles is

$\begin{gathered} A_(2\Delta)=2((bh)/(2)) \\ A_(2\Delta)=bh \\ A_(2\Delta)=6\cdot8=48in^2 \end{gathered}$

Next you have to calculate the ares of the rectangular faces:

One face has a length of 12 in and a width of 10 in, its area is:

$A=w\cdot l=10\cdot12=120in^2$

The second face has a width of 8in and a length of 12 in

$A=w\cdot l=8\cdot12=96in^2$

And the third face has a width of 6in and a length of 12 in

$A=w\cdot l=6\cdot12=72in^2$

Now all that is left to do is to add all calculates areas to determine the area od the prism

$A_{\text{prism}}=48+120+96+72=336in^2$

The option that best represents the area of the prism is C. 284in²

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