What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?(1 point) Responses 900 cm2 900 cm squared 1,368.06 cm2 1,368.06 cm squared 8,208.36 cm2 8,208.36 cm squared 1,350 cm2

1 answer

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

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

Where:

  • \( l \) is the length,
  • \( w \) is the width,
  • \( h \) is the height.

In this case, if all edge lengths are equal (since each edge length measures 15.10 cm), we can denote the edge length as \( a = 15.10 , \text{cm} \). Thus, for a cube (which is a special case of a rectangular prism):

\[ l = w = h = a = 15.10 , \text{cm} \]

Substituting into the formula:

\[ \text{Surface Area} = 2(a^2 + a^2 + a^2) = 2(3a^2) = 6a^2 \]

Now, substituting the value of \( a \):

\[ \text{Surface Area} = 6(15.10^2) \]

Calculating \( 15.10^2 \):

\[ 15.10^2 = 228.01 \]

Now multiply by 6:

\[ \text{Surface Area} = 6 \times 228.01 = 1368.06 , \text{cm}^2 \]

So, the surface area of the right rectangular prism is 1,368.06 cm².

The correct response is 1,368.06 cm².