Question

The net of a rectangular prism and its dimensions are shown in the diagram. 7.5 in. 7.5 in. 3 in. 3 in. 11.5 in. 1115 in What is the total surface area of the rectangular prism in square inches?

Answer 1

A rectangular prism is composed of 6 rectangular faces. The opposite faces of the prism are equal, which means that it has 3 pairs of congruent rectangles.

1) 2 rectangular faces have length l=11.5in and width w=7.5in

2) 2 rectangular faces have length l=11.5in and width w=3in

3) 2 rectangular faces have length l= 7.5in and width w=3in

To determine the total surface area of the prism, you have to calculate the area of each rectangular face and add them together.

The area of one rectangle can be calculated using the following formula

`A=w\cdot l`

So the area of each rectangular face is:

`A_1=w\cdot l=7.5\cdot11.5=86.25in^2`
`A_2=w\cdot l=\text{ 3}\cdot11.5=34.5in^2`
`A_3=w\cdot l=3\cdot7.5=22.5in^2`

To calculate the surface area of the rectangular prism you have to add twice the calculated areas (remember there are two congruent rectangles of each)

`\begin{gathered} SA=2A_1+2A_2+2A_3 \\ SA=2\cdot86.25+2\cdot34.5+2\cdot22.5 \\ SA=286.5in^2 \end{gathered}`

The surface area of the rectangular prism is 286.5in²