Question

Find the surface are of a rectangular prism.

Length:10in
Width:5 1/2in
Height:6 1/4

Answer 1

The answer to this problem is 318.75

Answer 2

Let's begin with covering some basics.

ヽ A rectangular prism has two ends and four sides (total of six faces)
ヽ Sides opposite each other have equal areas
ヽ The surface area is the sum of the areas of all six faces

To find the surface area of a rectangular prism, we need to find the of the different faces of the prism itself.

We can split these six faces into three different areas, as sides opposite each other have equal areas.

〜 Finding the area of two sides
We can find the area of two sides by doing:

2 ( Length x Height )
2 ( 10 x 6
`(1)/(4)` )
= 125 inches²

〜 Finding the area of the adjacent sides
We can find the area of these sides by doing:

2 ( Width x Height )
2 (5
`(1)/(2)` x 6
`(1)/(4)` )
= 68.75 inches²

〜 Finding the area of the ends
We can find the area of the ends sides by doing:

2 ( Length x Width )
2 ( 6
`(1)/(4)` x 10 )
= 125 inches²

〜 Finding the total surface area
Finally, we can add the three areas we've found together to find the total surface area of the rectangular prism.

125 + 68.75 + 125 = 318.75 inches²

The total surface area of this rectangular prism is 318.75 inches².

Hope this helps! ッ