Remember when we learned about exponents and we said “squared” when a number was to the power of 2? That is because of area. When you find the area of a square, you multiply the length and width, which are the same, so you end up with the side length to the 2 power, or the side length squared.

1. Each side of a small square mirror is \(12\text{ cm}\) long. Find the area of the mirror.
2. A rectangular rug measures \(4\text{ yd}\) by \(3\text{ yd}\). Find the area of the rectangle defined by this rug.
3. The top of a rectangular desk has a length of \(83\text{ cm}\) and a width of \(33\text{ cm}\). Find the area of the rectangle defined by this desk.
4. A dollar bill that is rectangular in shape has a length of \(6\text{ in}\) and a width of \(3\text{ in}\). Find the area of the rectangle defined by this dollar bill.
5. The lengths of two adjacent sides of a rectangular envelope are \(225\text{ mm}\) and \(28\text{ mm}\). Find the area of the rectangle defined by this envelope.
6. A rectangular garage door has a length of \(16\text{ ft}\) and a height of \(7\text{ ft}\). Find the area of the rectangle defined by this garage door.
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Solutions

1. \(144\text{ cm}^{2}\)
2. \(12\text{ yd}^{2}\)
3. \(2739\text{ cm}^{2}\)(Written Solution)

   The sides of the desk have been measured in centimeters.

   

   When we find the area of a rectangle, we are trying to find out how many square units are in the rectangle. In this case, we are measuring the area in centimeters, so we want to find out how many one-centimeter by one-centimeter squares are in the rectangle.

   

   To find the area of the top of the desk we will multiply the length by the width.

   \({\color{Red} 83} \times {\color{Cyan} 33} = 2739\)

   So the area of the top of the desk is \(2739\text{ cm}^{2}\)

4. \(18\text{ in}^{2}\) (Solution Video | Transcript)
5. \(6300\text{ mm}^{2}\) (Solution Video | Transcript)
6. \(112\text{ ft}^{2}\) (Written Solution)

   The garage door has been measured in feet.

   

   When we find the area of a rectangle, we are trying to find out how many unit squares are in that rectangle. In this case, we are measuring the area in feet, so we want to find out how many 1 foot by 1 foot squares are in the rectangle.

   

   To find the area of the garage door we need to multiply the length by the width.

   \({\color{Red} 16} \times {\color{Cyan} 7} = 112\)

   So the area of the garage door is \(112\text{ ft}^{2}\)