Question

What is the surface area of the triangular prism shown?

Answer 1

Answer:

The first step that we are going to do is to solve the area of the top rectangle.  We are given a width of 15 cm and a length of 25 cm so we can just multiply them against each other to get the area.

$Area = l * w$

$Area = 25\ cm * 15\ cm$

$Area = 375\ cm^2$

The second side that we are going to solve for is the bottom rectangle.  We are given a width of 12 cm and a length of 25 cm so lets just multiply them against each other to get the area.

$Area = l * w$

$Area = 25\ cm * 12\ cm$

$Area = 300\ cm^2$

The next area that we are going to determine is the back rectangle which has a width of 9 cm and a length of 25 cm so lets just multiply them against each other to get the area.

$Area = l * w$

$Area = 25\ cm * 9\ cm$

$Area = 225\ cm^2$

The final area that we have to determine are the side triangles.  After determining the area of one triangle we will have to multiply it by 2 to get the area for both of the triangles.  We are given a base of 12 cm and a height of 9 cm so lets just use the formula to find the area.

$Area = \frac{1}{2}* b*h$

$Area = \frac{1}{2}* 12\ cm*9\ cm$

$Area = 54\ cm^2$

Multiply it by two to get the area for both of the triangles.

$Area = 54\ cm^2 * 2$

$Area = 108\ cm^2$

Finally, we are onto the last part which is to add up all of the areas and get the surface area after we combine everything.

$Area_{total}=375\ cm^2 + 300\ cm^2 + 225\ cm^2 + 108\ cm^2$

$Area_{total}=1008\ cm^2$

Therefore, our final answer is option B, 1008 $cm^2$

Hope this helps!