Skill: Find missing dimensions from area

Explanation and Free Practice Resources

For rectangular regions measured in whole-number units, the missing length or width is found by relating area to the product of the two dimensions: unknown side = area ÷ known side. An area model or array connects the quotient to equal rows or columns, while multiplication verifies the result and distinguishes area from perimeter; more advanced cases involving fractional or decimal dimensions, nonrectangular shapes, or generalized algebraic formulas are not included.

Detailed Explanation: Find missing dimensions from area

The area of a rectangle tells how many square units cover it. For a rectangle,

area=length×width.\text{area}=\text{length}\times\text{width}.

If one side is missing, divide the area by the known side:

missing side=area÷known side.\text{missing side}=\text{area}\div\text{known side}.

Example: A rectangular garden has an area of 2424 square meters. Its length is 66 meters. What is its width?

  1. Write what you know:

area=24,length=6,width=?\text{area}=24,\qquad \text{length}=6,\qquad \text{width}=?
  1. Divide the area by the known length:

24÷6=424\div 6=4
  1. The width is 44 meters.

You can picture this as an array with 66 columns and 44 rows. It has 2424 squares altogether.

Check your answer with multiplication:

6×4=246\times 4=24

Since the product matches the area, the width is correct. Remember, area uses multiplication of the two side lengths; it is not the distance around the rectangle, which is the perimeter.

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Cartesian Grid - Rectangle Area and Dimension to Dimension - Positive Only


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