Surface Area of Right Rectangular Prisms Quick Check

Question

2 of 52 of 5 Items
Question
Use the formula to determine the surface area of a right rectangular prism where each edge length measures 12.75 cm.(1 point)
Responses

459 cm2
459 cm squared

975.38 cm2
975.38 cm squared

5,852.25 cm2
5,852.25 cm squared

76.5 cm2

Answer 1

To find the surface area of a right rectangular prism, we use the formula:

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

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

In this case, since all edges measure 12.75 cm, we have:

• \( l = 12.75 , \text{cm} \)
• \( w = 12.75 , \text{cm} \)
• \( h = 12.75 , \text{cm} \)

Now, we plug in these values into the formula:

\[ \text{Surface Area} = 2(12.75)(12.75) + 2(12.75)(12.75) + 2(12.75)(12.75) \]

\[ = 2(12.75 \cdot 12.75 + 12.75 \cdot 12.75 + 12.75 \cdot 12.75) \]

\[ = 2(3 \cdot (12.75)^2) \]

Now, calculate \( (12.75)^2 \):

\[ (12.75)^2 = 162.5625 \]

Then multiply by 3:

\[ 3 \cdot 162.5625 = 487.6875 \]

Now, multiply by 2:

\[ \text{Surface Area} = 2 \cdot 487.6875 = 975.375 , \text{cm}^2 \]

Therefore, rounding off, the surface area is \( 975.38 , \text{cm}^2 \).

The correct response is:

975.38 cm²