Surface area of a rectangular prism, step by step
A box has six faces in three matching pairs, so its surface area is twice the front plus twice the side plus twice the top.
The question
cm²
Surface area of a 5 × 5 × 13 box
5 × 5 × 13 cm
front and back:2 × 5 × 13 =130
front and back:2 × 5 × 13 =130
the two sides:2 × 5 × 13 =130
front and back:2 × 5 × 13 =130
the two sides:2 × 5 × 13 =130
top and bottom:2 × 5 × 5 =50
front and back:2 × 5 × 13 =130
the two sides:2 × 5 × 13 =130
top and bottom:2 × 5 × 5 =50
total:310
- Six faces, and the drawing can only show you three of them. The three you cannot see are the reason the usual wrong answer here is five faces added perfectly.
- Front and back are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.
- The two sides are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.
- Top and bottom are 5 by 5, and they are identical — so that pair is 2 × 5 × 5 = 50.
- Three pairs, six faces, none missed: 130 + 130 + 50 = 310 square cm.
How it works.
- 01
Six faces, and the drawing can only show you three of them. The three you cannot see are the reason the usual wrong answer here is five faces added perfectly.
- 02
Front and back are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.
- 03
The two sides are 5 by 13, and they are identical — so that pair is 2 × 5 × 13 = 130.
- 04
Top and bottom are 5 by 5, and they are identical — so that pair is 2 × 5 × 5 = 50.
- 05
Three pairs, six faces, none missed: 130 + 130 + 50 = 310 square cm.