To determine the surface area of a right rectangular prism (also known as a rectangular box), you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
In this case, each edge length of the prism measures 12.75 cm, which means:
- \( l = 12.75 \) cm
- \( w = 12.75 \) cm
- \( h = 12.75 \) cm
Now, let's calculate the surface area step by step.
-
Calculate \( lw \): \[ lw = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \]
-
Calculate \( lh \): \[ lh = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \]
-
Calculate \( wh \): \[ wh = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \]
-
Now, sum \( lw + lh + wh \): \[ lw + lh + wh = 162.5625 + 162.5625 + 162.5625 = 487.6875 , \text{cm}^2 \]
-
Multiply by 2 to get the total surface area: \[ \text{Surface Area} = 2 \times 487.6875 = 975.375 , \text{cm}^2 \]
So, the surface area of the right rectangular prism is 975.38 cm².
The correct response is:
- 975.38 cm²
- 975.38 cm squared
1 answer