Question

Which choice best represents the surface area of the triangle prism shown below?A: 264 square inchesB: 240 square inchesC: 284 square inchesD: 260 square inches

Answer 1

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

$A=\frac{bh}{2}$

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

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

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