The surface area of a rectangular prism with length \( I \), width \( w \), and height \( h \) is \( 2 l w+2 w h+ \) \( 2 l h \). Reba painted a box shaped like a rectangular prism for her little sister to use as a treasure box. The treasure box is 12 inches long, 5 inches wide, and 4 inches high. What is the surface area of the treasure box? Write your answer as a whole number or decimal. submit

To find the surface area of Reba's treasure box, plug the dimensions into the surface area formula: \[ \text{Surface Area} = 2lw + 2wh + 2lh \] Here, \( l = 12 \) inches, \( w = 5 \) inches, and \( h = 4 \) inches. Calculating each term: 1. \( 2lw = 2 \times 12 \times 5 = 120 \) square inches 2. \( 2wh = 2 \times 5 \times 4 = 40 \) square inches 3. \( 2lh = 2 \times 12 \times 4 = 96 \) square inches Now, add them together: \[ \text{Total Surface Area} = 120 + 40 + 96 = 256 \text{ square inches} \] So, the surface area of the treasure box is **256 square inches**. --- Did you know that the concept of surface area was utilized by ancient civilizations, such as the Egyptians, to design their monumental structures? These engineers understood that the exterior space was vital not just for aesthetics but also for calculating the quantity of materials needed! Moreover, when Reba completes her treasure box, she can use it for all sorts of creative activities! She can turn it into a decorative storage unit for art supplies, a place for keepsakes, or even a unique gift box for special occasions. Painting and decorating can also be an engaging activity for her and her sister!