To find the surface area of a rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2(ab + bc + ca) \]
where \(a\), \(b\), and \(c\) are the dimensions of the rectangular prism.
Given the dimensions:
- \(a = 3 \frac{3}{4} \text{ dm} = \frac{15}{4} \text{ dm}\)
- \(b = 4 \frac{1}{2} \text{ dm} = \frac{9}{2} \text{ dm}\)
- \(c = 5 \text{ dm}\)
First, let's convert these fractions to decimals for easier calculation:
\[ a = 3 \frac{3}{4} = 3.75 \text{ dm} \]
\[ b = 4 \frac{1}{2} = 4.5 \text{ dm} \]
\[ c = 5 \text{ dm} \]
Next, calculate each product:
\[ ab = 3.75 \times 4.5 = 16.875 \]
\[ bc = 4.5 \times 5 = 22.5 \]
\[ ca = 3.75 \times 5 = 18.75 \]
Summing these:
\[ ab + bc + ca = 16.875 + 22.5 + 18.75 = 58.125 \]
Now multiply by 2 to find the total surface area:
\[ \text{Surface Area} = 2 \times 58.125 = 116.25 \text{ square decimeters} \]
So the surface area of the rectangular prism is:
\[ 116 \frac{1}{4} \text{ dm}^2 \]
Let's match the answer with the available options:
- 116.25 dm² = 116 ¼ dm²
Therefore, the correct answer is \( 116 \frac{1}{4} \text{ dm}^2 \).
What is the surface area of a rectangular prism whose dimensions are 3 3/4 dm× 4 1/2 dm×5 dm in square decimeters?(1 point)
Responses
11614 dm2
116 Start Fraction 1 over 4 End Fraction dm squared
8438 dm2
84 Start Fraction 3 over 8 End Fraction dm squared
5818 8 dm2
58 Start Fraction 1 over 8 End Fraction dm squared
16 dm2
1 answer