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Florida Grade 4 Math · Geometric Reasoning

MA.4.GR.2.2: Same Perimeter or Same Area

What this Grade 4 benchmark means, worked examples, common mistakes, and a free printable worksheet.

Created by a Florida mom · Published by Tropical Learning LLC

Download Free Worksheet (PDF)See worked examples

What Is Benchmark MA.4.GR.2.2?

Students solve problems with rectangles that have the same perimeter but different areas, or the same area but different perimeters. All side lengths are whole numbers.

For example, a rectangle with an area of 24 square feet could be 6 feet by 4 feet or 8 feet by 3 feet. Same area doesn't mean same perimeter, and same perimeter doesn't mean same area.

Official benchmarkSolve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters.

On the FAST test: part of the Grade 4 reporting category Geometric Reasoning, Measurement, and Data Analysis and Probability, which is about 31–37% of the test.

Worked Examples

Worked Example 1

Same Area, Different Perimeters

List rectangles with whole-number sides and an area of 24 square units, and find each perimeter.
  1. 11 × 24: perimeter 1 + 24 + 1 + 24 = 50 units
  2. 22 × 12: perimeter 2 + 12 + 2 + 12 = 28 units
  3. 33 × 8: perimeter 3 + 8 + 3 + 8 = 22 units
  4. 44 × 6: perimeter 4 + 6 + 4 + 6 = 20 units
Answer: The perimeters are 50, 28, 22, and 20 units.

Worked Example 2

Same Perimeter, Different Areas

Three rectangles each have a perimeter of 20 units: 9 by 1, 7 by 3, and 5 by 5. Which has the greatest area?
  1. 19 × 1 = 9 square units
  2. 27 × 3 = 21 square units
  3. 35 × 5 = 25 square units
Answer: 5 by 5 (25 square units)

Common Mistakes to Watch For

Thinking the same area means the same perimeter

Wrong:6 by 4 and 8 by 3 both have an area of 24, so their perimeters are equal.

6 by 4 has a perimeter of 20 units, and 8 by 3 has a perimeter of 22 units.

Thinking the same perimeter means the same area

Wrong:9 by 1 and 5 by 5 both have a perimeter of 20, so they cover the same space.

9 by 1 covers 9 square units, and 5 by 5 covers 25 square units.

Helpful Math Tip

Cut out 24 paper squares and arrange them into every possible rectangle. Count the squares (area) and the edges (perimeter) each time.

Related Grade 4 Skills

MA.4.GR.2.1

Perimeter and Area With Unknown Sides

MA.4.AR.3.1

Factors, Prime, and Composite Numbers

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Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.