Question

I need help on finding the surface area ona rectangle prism

Answer 1

The rectangular prism has 6 rectangular faces, the opposite faces of the prism are equal, which means that you have 3 pairs of equal rectangles that conform to the shape.

To determine the surface area of the rectangular prism you have to add the area of each face.

The rectangular prism has a determined width, length, and height.

To calculate the area of the top and bottom faces, you have to multiply the width and length of the prism.

`A_1=(w\cdot l)_{}`

To calculate the area of the front and back faces, you have to multiply the length and height of the prism.

`A_2=(l\cdot h)`

To calculate the area of the lateral faces you have to multiply the width and height of the prism.

`A_3=(w\cdot h)`

Since there are two equal faces of each, you have to multiply the three terms by 2 and then add them to calculate the total area:

`\begin{gathered} A_{\text{total}}=2A_1+2A_2+2A_3 \\ A_{\text{total}}=2(w\cdot l)+2(l\cdot h)+2(w\cdot h) \end{gathered}`

The length of the prism is l=9m

The height of the prism is h=2m

The width of the prism is w=6m

You can calculate the surface area as:

`\begin{gathered} A_{\text{total}}=2(6\cdot9)+2(9\cdot2)+2(6\cdot2) \\ A_{\text{total}}=168m^2 \end{gathered}`

The surface area of the rectangular prism is 168m²