Question

What is the surface area of the triangular prism shown?

Answer 1

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 = (1)/(2)* b*h`

`Area = (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!