Question

landon is decorating the outside of a box in the shape of a right rectangular prism. the figure below shows a net for the box. what is the surface area of the box, in square centimeters, that landon decorates? answer attempt 1 out of 3 ( a=square mathrm{cm}^{2} ) submit answer copyright ( odot 2025 ) deltamath.com all rights reserved. deltamath.com

Explanation:

Step1: Calculate the area of each type of rectangle

The formula for the area of a rectangle is \(A = l\times w\).

• For rectangles with \(l = 15\mathrm{cm}\) and \(w = 9\mathrm{cm}\), \(A_1=15\times9 = 135\mathrm{cm}^2\)
• For rectangles with \(l = 9\mathrm{cm}\) and \(w = 9\mathrm{cm}\), \(A_2=9\times9=81\mathrm{cm}^2\)
• For rectangles with \(l = 15\mathrm{cm}\) and \(w = 5\mathrm{cm}\), \(A_3 = 15\times5=75\mathrm{cm}^2\)

Step2: Count the number of each type of rectangle

• Rectangles with \(A_1\): There are \(2\) of them.
• Rectangles with \(A_2\): There are \(2\) of them.
• Rectangles with \(A_3\): There are \(2\) of them.

Step3: Calculate the total surface area

The total surface area \(S\) of the rectangular prism (sum of the areas of all 6 faces) is \(S=2\times A_1 + 2\times A_2+2\times A_3\)

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Answer:

\(582\)