Question

1. a gift box will be made from a rectangular piece of cardboard measuring 12 inches by 20 inches, with squares cut out of the corners of the sides, as shown. the sides of the squares are 3 inches. find the area of the cardboard after the corners are cut out.

Explanation:

Step1: Calculate original area

The original area of the rectangular cardboard is the product of its length and width. The length $l = 20$ inches and the width $w=12$ inches. So the original area $A_{original}=l\times w=20\times12 = 240$ square - inches.

Step2: Calculate area of one square

The area of a square is given by the formula $A_{square}=s^2$, where $s = 3$ inches. So $A_{square}=3^2=9$ square - inches.

Step3: Calculate total area of 4 squares

Since there are 4 squares cut out from the corners, the total area of the 4 squares is $A_{total\ of\ squares}=4\times A_{square}=4\times9 = 36$ square - inches.

Step4: Calculate remaining area

The area of the cardboard after the corners are cut out is $A = A_{original}-A_{total\ of\ squares}=240 - 36=204$ square - inches.

Answer:

204 square inches