What is the surface area of a rectangular prism

where each edge length measures 15.1 cm?
*Hint: Don't forget to use your Desmos calculator and
STAAR Reference Sheet to help!
(1 point)
1,350 cm
2
900 cm2
1,368.06 cm2
8,208.36 cm

1 answer

The surface area \( S \) of a rectangular prism can be calculated using the formula:

\[ S = 2lw + 2lh + 2wh \]

where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism.

In this case, since all edges are equal (the prism is a cube), each edge length is \( 15.1 \) cm. Therefore, we have:

  • \( l = 15.1 , \text{cm} \)
  • \( w = 15.1 , \text{cm} \)
  • \( h = 15.1 , \text{cm} \)

Now plug in the values:

\[ S = 2(15.1)(15.1) + 2(15.1)(15.1) + 2(15.1)(15.1) \]

This simplifies to:

\[ S = 6 \times (15.1 \times 15.1) \]

Calculating \( 15.1 \times 15.1 \):

\[ 15.1 \times 15.1 = 228.01 , \text{cm}^2 \]

Now multiply by 6:

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

Thus, the surface area of the rectangular prism is:

\[ \boxed{1368.06 , \text{cm}^2} \]