Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Perimeter is the distance all the way around a flat shape. For any polygon, students find it by adding the lengths of every side, so a triangle with sides 5, 7 and 9 centimeters has a perimeter of 21 centimeters. Perimeter is a length, measured in units like inches or meters, not in square units.
Third graders go further than adding sides. They find an unknown side when the perimeter is given, using subtraction or reasoning about equal sides in rectangles and squares. They also explore a surprising relationship: rectangles can share the same perimeter but have different areas, or share the same area but have different perimeters. A 1-by-11 rectangle and a 6-by-6 square both have a perimeter of 24 units, yet one has an area of 11 square units and the other 36. Investigating this helps students separate the two ideas firmly, and it connects to real choices like fencing a garden to enclose the most space.
Students multiply length by width when asked for perimeter. Trace around the edge with a finger and say "distance around" each time.
For a rectangle labeled 8 and 3, some students add only 8 + 3 = 11. All four sides count: 8 + 3 + 8 + 3 = 22.
Many students assume shapes with equal perimeters cover the same space. Build rectangles with a fixed loop of string to see the area change.
Writing 22 square units for a perimeter shows the ideas are blurred. Perimeter is a length in units.
A quadrilateral has a perimeter of 30 inches. Three of its sides are 6 inches, 9 inches and 7 inches. How long is the fourth side?
Answer: The missing side is 8 inches long.
Use geoboards or grid paper to build rectangles with a fixed perimeter, recording each one's dimensions and area in a table. Students quickly see the pattern that long, thin rectangles have small areas. Walking around the edge of the playground or classroom gives perimeter a physical meaning.
Assessment items ask for perimeter from labeled sides, a missing side, or which rectangles share a perimeter or area. Questions that show two shapes and ask which has the greater perimeter test whether students keep the two measures separate.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 21 (also accepted: 21 cm)
Add all three sides: 5 + 7 + 9 = 21 cm.
Answer: 22 (also accepted: 22 meters, 22 m)
Opposite sides of a rectangle are equal: 8 + 3 + 8 + 3 = 22 meters.
Answer: 7 (also accepted: 7 inches)
A square has 4 equal sides, so each side is 28 ÷ 4 = 7 inches.
Answer: D) 4 by 8
The square's perimeter is 24. A 4-by-8 rectangle has 4 + 8 + 4 + 8 = 24 too, though its area is 32, not 36.
Answer: C) The 2-by-6 rectangle has the larger perimeter
2 + 6 + 2 + 6 = 16 and 3 + 4 + 3 + 4 = 14. Same area, but the longer, thinner rectangle has the larger perimeter.
Answer: 6 (also accepted: 6 feet)
Known sides: 7 + 9 + 8 + 10 = 34. 40 - 34 = 6 feet.
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
A full lesson with slides, activities and an exit ticket on perimeter of polygons, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.MD.D.8 with an answer key, ready in about a minute.
Make a worksheet →Turn perimeter of polygons into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Perimeter is the distance around a shape, measured in units of length. Area is the surface inside, measured in square units. The standard asks students to compare rectangles where one measure is fixed and the other changes.
They add side lengths and may notice shortcuts for rectangles and squares. A general formula is applied in 4.MD.A.3.