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

975.38 cm2
975.38 cm squared

5,852.25 cm2
5,852.25 cm squared

76.5 cm2
76.5 cm squared

459 cm2
459 cm squared

Answer 1

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

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

where \(l\), \(w\), and \(h\) are the lengths of the edges of the prism. In this case, since each edge length measures 12.75 cm, we have:

• Length (l) = 12.75 cm
• Width (w) = 12.75 cm
• Height (h) = 12.75 cm

Now, we can substitute these values into the formula:

1. Calculate \(lw\): \[ lw = 12.75 \times 12.75 = 162.5625 \text{ cm}^2 \]

2. Calculate \(lh\): \[ lh = 12.75 \times 12.75 = 162.5625 \text{ cm}^2 \]

3. Calculate \(wh\): \[ wh = 12.75 \times 12.75 = 162.5625 \text{ cm}^2 \]

Now, substitute these values into the surface area formula:

\[ \text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625) \] \[ \text{Surface Area} = 2(487.6875) = 975.375 \text{ cm}^2 \]

Since the question asks for the surface area, the closest answer is

975.38 cm² or 975.38 cm squared.