Question

Kym’s play tent for her doll is 39 inches tall, 27 inches long, and 19 inches wide. Its diagonal measurement, or the hypotenuse, is 40.14 inches. What is its total surface area? Round your answer to the nearest hundredth.(1 point)
in.2

Answer 1

To calculate the total surface area of Kym's play tent, which is shaped like a rectangular prism, we can use the formula for the surface area of a rectangular prism:

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

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

Given:
- \( l = 27 \) inches
- \( w = 19 \) inches
- \( h = 39 \) inches

Now, we will plug in these values into the surface area formula:

1. Calculate the area of each component:
- \( lw = 27 \times 19 = 513 \) square inches
- \( lh = 27 \times 39 = 1053 \) square inches
- \( wh = 19 \times 39 = 741 \) square inches

2. Now, sum these areas:
\[
lw + lh + wh = 513 + 1053 + 741 = 2307 \text{ square inches}
\]

3. Finally, multiply by 2 to find the total surface area:
\[
\text{Surface Area} = 2 \times 2307 = 4614 \text{ square inches}
\]

So, the total surface area of Kym's play tent is:

\[
\boxed{4614} \, \text{in}^2
\]

There are no decimal places needed, as rounding to the nearest hundredth would yield the same whole number answer.