Find missing rectangle or square dimensions from area or perimeter

What you will learn

• Find missing rectangle or square dimensions from area or perimeter

Models used: number sentences, stories, tables.

Before you start

• Find areas of rectangles and squares

How many squares in each row?

A rectangle covers 24 square units. It has four equal rows.

1. All the small boxes represent equally sized units, even when they belong to different rows.

   A rectangle covers 24 square units. It has four equal rows.

   One unit must have the same value in every row. That lets us compare amounts by counting their units.

   Rows

   4 equal units · 4 units = 24

2. 4 rows run across the picture; each row contains 6 objects.

   Share the 24 squares equally between those four rows. There are six in each row.

   24 ÷ 4 = 6

   4 rows of 6 = 4 × 6 = 24

3. Each little square is one square unit. There are 6 squares across and 4 rows.

   Six squares in each row means the missing length is 6 units.

   6 × 4 = 24

Worked example: A new example, together

A rectangle has area 15 cm² and width 3 cm. Find its length.

1. Recover a missing dimension. Read each value with the heading above its column.

   Identify the surface to cover and the lengths that determine its rows. Keep missing or overlapping pieces visible.

   The same area or perimeter relationship can be used in reverse.

   Recover a missing dimension

   Given measure	Known dimension
   15	3 cm

2. Recover a missing dimension. Read each value with the heading above its column.

   Area = length × width.

   Recover a missing dimension

   Given measure	Known dimension
   15	3 cm

   A rectangle has area 15 cm² and width 3 cm. Find its length.

   5 cm

3. Recover a missing dimension. Read each value with the heading above its column.

   Length = 15 ÷ 3.

   Recover a missing dimension

   Given measure	Known dimension
   15	3 cm

4. Recover a missing dimension. Read each value with the heading above its column.

   Length = 5 cm.

   Recover a missing dimension

   Given measure	Known dimension
   15	3 cm

5. Recover a missing dimension. Read each value with the heading above its column.

   Check the result against the question we started with.

   5 × 3 = 15.

   We found 5 cm. The same area or perimeter relationship can be used in reverse.

   Recover a missing dimension

   Given measure	Known dimension
   15	3 cm

Common mistakes to discuss

• Halving the perimeter gives the length. Half the perimeter is one length plus one width. With perimeter 22 cm and width 6 cm, the length is 11 − 6 = 5 cm.

Check your understanding

• Find missing rectangle or square dimensions from area or perimeter
• explain area calculations using covered square units
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.