Word problem using Singapore math

Question

A rectangular picture measures 82cm by 75cm. It has a a 7cm border Wide around it. What is the area of the border.

Answer 1

I think that the easiest way to do this would be to find the total area of the picture, including the border, and then subtract out the area of the smaller rectangle within the frame that consists of only the picture, and not the border.

The first step would be to calculate the area of the rectangle, which is equal to the length x width. In this case, it is 82cm x 75cm, which is equal to 6150cm. Since we know that the border is 7cm wide around the entire picture, the area of the image itself is only (82-14)cm x (75-14)cm. This is easiest to conceptualize if you draw out the frame - the border on each side is equal to 7cm, so the length decreases by the border on the top plus the border on the bottom, which is 14cm. The same thing happens with the width. The inner picture therefore has an area of 68cm x 61cm, which is equal to 4148cm. The border will be the difference between the entire frame and the inner picture, which is 6150cm - 4148cm = 2002cm.