Question

which expression represents the total surface area of the prism shown? 5(5)+7(7)+10(10) 2(5·5)+2(7·7)+2(10·10) 2(5·7)+2(5·10)+2(7·10) 5(7)+5(10)+7(10)

Explanation:

Step1: Recall the formula for the surface area of a rectangular prism.

The formula for the total surface area (SA) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( SA = 2(lw + lh + wh) \).

Step2: Identify the length, width, and height of the prism.

From the diagram, the dimensions are \( l = 7 \) in, \( w = 5 \) in, and \( h = 10 \) in.

Step3: Substitute the dimensions into the formula.

Substituting \( l = 7 \), \( w = 5 \), and \( h = 10 \) into the formula \( SA = 2(lw + lh + wh) \), we get:
\( SA = 2(7 \cdot 5 + 7 \cdot 10 + 5 \cdot 10) \)
Which can be rewritten as \( 2(5 \cdot 7) + 2(5 \cdot 10) + 2(7 \cdot 10) \) (since multiplication is commutative, \( 7 \cdot 5 = 5 \cdot 7 \), \( 7 \cdot 10 = 10 \cdot 7 \), etc.).

Answer:

\( 2(5 \cdot 7) + 2(5 \cdot 10) + 2(7 \cdot 10) \) (the third option: \( 2(5 \cdot 7) + 2(5 \cdot 10) + 2(7 \cdot 10) \))