Question

joe wants to paint the outside of a wooden box. he needs to find the surface area of the box in order to buy paint. a net of the box is shown. what is the surface area of the box? 4 ft 2 ft top 1 1/2 ft back left bottom right front 34 ft² 17 ft² 12 ft² 28 ft²

Explanation:

Step1: Identify the dimensions of the box

The box is a rectangular prism. From the net, we can see the length \( l = 4\) ft, the height \( h = 2\) ft, and the width \( w = 1\frac{1}{2}=\frac{3}{2}\) ft.

Step2: Recall the formula for the surface area of a rectangular prism

The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \).

Step3: Calculate each term

• Calculate \( lw \): \( lw=4\times\frac{3}{2} = 6\) square feet.
• Calculate \( lh \): \( lh = 4\times2=8\) square feet.
• Calculate \( wh \): \( wh=\frac{3}{2}\times2 = 3\) square feet.

Step4: Substitute into the formula

Substitute the values of \( lw \), \( lh \), and \( wh \) into the surface - area formula:
\( SA=2(6 + 8+3)\)
First, add the terms inside the parentheses: \( 6 + 8+3=17\)
Then, multiply by 2: \( SA = 2\times17=34\) square feet.

Answer:

\(34\space ft^{2}\)