Question

Find the surface area of a box that measures 10 cm wide, 4 cm high, 17 cm long.

Answer 1

To find the surface area of a rectangular box (also known as a rectangular prism), you can use the following formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the box.

Given:
- Length (\( l \)) = 17 cm
- Width (\( w \)) = 10 cm
- Height (\( h \)) = 4 cm

Now, let's calculate each term in the formula:

1. Calculate \( lw \):
\[
lw = 17 \, \text{cm} \times 10 \, \text{cm} = 170 \, \text{cm}^2
\]

2. Calculate \( lh \):
\[
lh = 17 \, \text{cm} \times 4 \, \text{cm} = 68 \, \text{cm}^2
\]

3. Calculate \( wh \):
\[
wh = 10 \, \text{cm} \times 4 \, \text{cm} = 40 \, \text{cm}^2
\]

Now, sum these results:
\[
lw + lh + wh = 170 \, \text{cm}^2 + 68 \, \text{cm}^2 + 40 \, \text{cm}^2 = 278 \, \text{cm}^2
\]

Finally, multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 278 \, \text{cm}^2 = 556 \, \text{cm}^2
\]

Therefore, the surface area of the box is \( \boxed{556} \, \text{cm}^2 \).