Use the formula for the surface area of a right rectangular prism to find the surface area of a shape with the following measurements: length = 4.5 cm, width = 3.5 cm, and height = 2.5 cm.(1 point)

Question

Responses

35.75 cm2
35.75 cm squared

63 cm2
63 cm squared

10.5 cm2
10.5 cm squared

71.5 cm2
71.5 cm squared

Answer 1

The formula for the surface area \( SA \) of a right rectangular prism is given by:

\[ SA = 2(lw + lh + wh) \]

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

Plugging in the given values:

• Length \( l = 4.5 \) cm
• Width \( w = 3.5 \) cm
• Height \( h = 2.5 \) cm

First, calculate each of the products:

1. \( lw = 4.5 \times 3.5 = 15.75 \) cm²
2. \( lh = 4.5 \times 2.5 = 11.25 \) cm²
3. \( wh = 3.5 \times 2.5 = 8.75 \) cm²

Now add these products together:

\[ lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 \text{ cm}^2 \]

Finally, multiply by 2 to find the surface area:

\[ SA = 2(35.75) = 71.5 \text{ cm}^2 \]

So the surface area of the right rectangular prism is:

\[ \boxed{71.5 , \text{cm}^2} \]