Finding the area of a rectangle means we’re finding how many unit squares make up the rectangle. The following video will go over how to do this.

Video Source (03:52 mins) | Transcript

\(Area = Length \times Width\)

We can only find the area if the two sides are measured in the same units and the units of our area will be in units squared (ex: \(inches^2, cm^2, \)etc.) because we are counting the number of unit squares within our area.

Real World Application

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.

Additional Resources

• Khan Academy: Introduction to Area (4:16 mins; Transcript)
• Khan Academy: Perimeter and Area (8:25 mins; Transcript)

Practice Problems

1. Each side of a small square mirror is 12 cm long. Find the area of the mirror. (
   Solution

   x

   Solution:
   \(144\text{ cm}^{2}\)
   )
2. A rectangular rug measures 4 yd by 3 yd. Find the area of the rectangle defined by this rug. (
   Solution

   x

   Solution:
   \(12\text{ yd}^{2}\)
   )
3. The top of a rectangular desk has a length of 83 cm and a width of 33 cm. Find the area of the rectangle defined by this desk. (
   Solution

   x

   Solution: \(2739\text{ cm}^{2}\)
   Details:
   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 \({\color{Red}length}\) by the \({\color{Cyan}width}\).
   
   \({\color{Red} 83} \times {\color{Cyan} 33} = 2739\)
   
   So the area of the top of the desk is \(2739\text{ cm}^{2}\).
   )
4. A dollar bill that is rectangular in shape has a length of 6 in and a width of 3 in. Find the area of the rectangle defined by this dollar bill. (
   Video Solution

   x

   Solution: \(18\text{ in}^{2}\)
   Details:
   

   
   (Video Source | Transcript)
   )
5. The lengths of two adjacent sides of a rectangular envelope are 225 mm and 28 mm. Find the area of the rectangle defined by this envelope. (
   Video Solution

   x

   Solution: \(6300\text{ mm}^{2}\)
   Details:
   

   
   (Video Source | Transcript)
   )
6. A rectangular garage door has a length of 16 ft and a height of 7 ft. Find the area of the rectangle defined by this garage door. (
   Solution

   x

   Solution: \(112\text{ ft}^{2}\)
   Details:
   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 \({\color{Red}length}\) by the \({\color{Cyan}width}\).
   
   \({\color{Red} 16} \times {\color{Cyan} 7} = 112\)
   
   So the area of the garage door is \(112\text{ ft}^{2}\).
   )

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