a box has dimensions 5cm,9cm,5cm. What is the surface area. Teacher did not specify which was length, width, height.

Question

Find the surface area of a box with dimensions 5cm,9cm,5cm. I don't know which dimension is length, width, height though.

Answer 1

Which number is the length, which is the width and which is the height does not matter. In a rectangular prism, the length, width, and height are interchangeable.

Assume the length is 9 cm, the width is 5 cm, and the height is 5 cm.

You have six rectangles: the top and bottom, the front and back, and the left and right sides.

The opposite rectangles are congruent and therefore have the same area.

9x5 for the top and bottom rectangles

9x5 for the left and right side rectangles

5x5 for the front and back rectangles

9x5=45 sq cm

9x5=45 sq cm

5x5=25 sq cm

2(45)=90 sq cm

2(45)=90 sq cm

2(25)=50 sq cm

90+90+50=230 sq cm

if you want a formula for surface area...

SA=2(lw)+2(lh)+2(wh)