Question

follow the steps to find the surface area of the rectangular prism. what is the area of the sides? top and bottom: 240 cm² front and back: 140 cm² sides: ? total sa: ?

Explanation:

Step1: Find the area of the sides

The sides of a rectangular prism are two congruent rectangles. The formula for the area of a rectangle is \(A = l\times w\). Here, the dimensions for the side - rectangles are \(7\mathrm{cm}\) (height) and \(12\mathrm{cm}\) (width).
The area of one side is \(A_1=7\times12 = 84\mathrm{cm}^2\).
The area of the two sides is \(A = 2\times(7\times12)\)

$$A=2\times84=168\mathrm{cm}^2$$

Step2: Find the total surface area (SA)

The total surface area of a rectangular prism is the sum of the areas of all its faces.
We know that the area of the top and bottom is \(240\mathrm{cm}^2\), the area of the front and back is \(140\mathrm{cm}^2\), and the area of the sides is \(168\mathrm{cm}^2\)

$$SA=240 + 140+168$$

$$SA=(240+140)+168$$

$$SA = 380+168$$

$$SA=548\mathrm{cm}^2$$

Answer:

The area of the sides is \(168\mathrm{cm}^2\) and the total surface area is \(548\mathrm{cm}^2\)