Question

A rectangular prism has dimensions of 2x, 3x, and 5x. Write an expression for the total surface area of the prism.

Answer 1

Check the picture below.

the left and right are just two rectangles of 5x * 2x

the front and back are just two rectangles of 3x * 5x

the top and bottom are also two rectangles of 3x * 2x

since the area of a rectangle is just width * length then,

$\bf \stackrel{left~right}{2(5x\cdot 2x)}~~+~~\stackrel{front~back}{2(3x\cdot 5x)}~~+~~\stackrel{top~bottom}{2(3x\cdot 2x)} \\\\\\ 2(10x^2)+2(15x^2)+2(6x^2)\implies 20x^2+30x^2+12x^2\implies 62x^2$