Question

5.2 length 5.2 width what's the height of rectangle. the total surface area is 220.48

Answer 1

To find the height of a rectangular prism (or box) given its length, width, and total surface area, we can use the formula for the surface area of a rectangular prism:

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

Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

Given:
- \( l = 5.2 \)
- \( w = 5.2 \)
- Surface Area = 220.48

Now, we can plug in the values into the formula:

\[
220.48 = 2(5.2)(5.2) + 2(5.2)(h) + 2(5.2)(h)
\]

Calculating \( 2(5.2)(5.2) \):

\[
2(5.2)(5.2) = 2 \times 27.04 = 54.08
\]

Now, substituting that back into the equation:

\[
220.48 = 54.08 + 4(5.2)(h)
\]

Subtract \( 54.08 \) from both sides:

\[
220.48 - 54.08 = 4(5.2)(h)
\]
\[
166.4 = 4(5.2)(h)
\]

Now, simplify:

\[
166.4 = 20.8h
\]

To find \( h \), divide both sides by \( 20.8 \):

\[
h = \frac{166.4}{20.8} = 8
\]

So, the height of the rectangular prism is \( \boxed{8} \).