Find the value of x given the surface area

Question

SA= 432 units ^2

6

_______

x/ /

————. | 12

| |. |

| | /

|______|/

It’s a rectangular prism

Answer 1

Hello, Fer,

If I understand the drawing, this is a rectangular box with height = 12, width = 6, and depth = x. It has 6 surfaces with a total surface area of 432 unit².

The 6 sides are comprised of 3 pairs. We can express the area of the three sides and then multiply each by 2 to obtain the total area:

The three expressions would be:

6x unit²

12 unit²

12x unit²

Multiply each by 2 to include the second, identical side:

12x unit²

24 unit²

24x unit²

Add these and set equal to 432 unit²

12x + 24 + 24x = 432 unit²

36x + 24 = 432 unit²

36x = 408 unit²

x = 11.3333 units

Bob