IXL | Rectangles: relationship between perimeter and area

The rectangles below have the same perimeter.

6 cm

3 cm

If the area of the gray rectangle is 8 square centimeters, what are its dimensions?

centimeters by centimeters

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Learn with an example

question

The rectangles below have the same area.

4 cm

If the perimeter of the green rectangle is 20 centimeters, what are its dimensions?

centimeters by centimeters

key idea

Rectangles with the same area can have different perimeters.

solution

Find the area of the red rectangle.

4 × 4 = 16

The green rectangle also has an area of 16.

Next make a list of possible dimensions for the green rectangle. List dimensions that give an area of 16. The first whole number that divides evenly into 16 is 1, so start with 1 by 16.

Dimensions	Area	Perimeter
1 by 16	1 × 16 = 16
2 by 8	2 × 8 = 16
4 by 4	4 × 4 = 16

Next find the perimeters.

Dimensions	Area	Perimeter
1 by 16	1 × 16 = 16	1 + 16 + 1 + 16 = 34
2 by 8	2 × 8 = 16	2 + 8 + 2 + 8 = 20
4 by 4	4 × 4 = 16	4 + 4 + 4 + 4 = 16

The problem says that the green rectangle has a perimeter of 20. So, its dimensions must be 2 by 8.

The green rectangle is 2 centimeters by 8 centimeters.

Looking for more? Try these:

Lesson: Area of rectangles

Lesson: Perimeter

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Teacher tools

Work it out

Not feeling ready yet? These can help:

II.9Relationship between area and perimeter

GG.1Perimeter

GG.2Area of rectangles and squares

AA.10Solve one-step equations with whole numbers

Lesson: Area of rectangles

Lesson: Perimeter

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