Question

karen wants to decorate her dresser by painting it a new color.
how many square feet does karen need to paint so all six sides of the dresser are painted?
image of a dresser with dimensions 3 ft (height), 4 ft (length), 2 ft (width)
karen needs to paint \boxed{} square ft so all six sides of the dresser are painted.

Explanation:

Step1: Recall Surface Area Formula

The dresser is a rectangular prism. The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l \) is length, \( w \) is width, and \( h \) is height. From the problem, \( l = 4 \) ft, \( w = 2 \) ft, \( h = 3 \) ft.

Step2: Calculate Each Pair of Faces

First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 4 \times 2 = 8 \)
• \( lh = 4 \times 3 = 12 \)
• \( wh = 2 \times 3 = 6 \)

Step3: Substitute into Formula

Substitute these values into the surface area formula:
\( SA = 2(8 + 12 + 6) = 2(26) = 52 \)

Answer:

52