Elementary geometry is the friendliest part of the math year and the one most likely to be taught as vocabulary. A student can name a rhombus, recite that a right angle is 90 degrees, and still have no idea whether to use perimeter or area to buy carpet. These four sheets are built the other way round: every one of them ends with a question that only makes sense if the student understands what the measurement is for.
All measurements are in inches, feet and yards, and areas in square inches and square feet. Everything is in US Letter and every sheet closes with an answer key that shows the working.
2D shapes: sides and cornersGrade 2 · 10 exercises + keyDownload PDF
PerimeterGrade 3 · 10 exercises + keyDownload PDF
Angles and trianglesGrade 4 · 10 exercises + keyDownload PDF
Area and perimeterGrade 5 · 10 exercises + keyDownload PDFHow we use these in class
Measure something real before the first worksheet. A desk, a book, the doorway. Perimeter and area stop being formulas about ten minutes after a student has walked the perimeter of the classroom with a tape measure and then covered part of the floor with sheets of paper.
Make the units carry the meaning. Perimeter is in inches; area is in square inches. If a student writes the wrong unit, they usually have the wrong concept, not a careless pen — so it is worth stopping on rather than correcting in passing.
Ask the "which would you need" question constantly. A fence goes around: that is perimeter. Paint covers: that is area. The last exercise of the Grade 5 sheet asks for both numbers about the same garden bed, with their units, which is the whole topic in one question.
Use the classroom as the shape bank. Grade 2 students find right angles faster in the room than on a page, and the ones they find are the ones they remember.
Four misconceptions worth heading off
"A square is not a rectangle." It is — a rectangle is any four-sided shape with four right angles, and a square meets that with sides that happen to be equal. Children resist this for a while, and the argument is worth having rather than settling by decree.
"A triangle standing on a point is not a triangle." Shapes get recognized in the orientation they were taught in. Rotating a shape on the board, or handing out cut-outs that can be turned, fixes this faster than any worksheet.
"Bigger perimeter means bigger area." It does not, and the two rectangles in exercise 7 of the Grade 5 sheet are there to prove it: same perimeter, different area.
"An angle is how long the lines are." Students often judge an angle by the length of the arms rather than the opening between them. Drawing the same angle twice, once with short arms and once with long ones, settles it in about a minute.
A note on the sequence
Grade 2 is naming and counting: sides, corners, flat against solid. Grade 3 introduces perimeter as an addition problem, which is exactly what it is. Grade 4 brings angles and the classification of triangles. Grade 5 brings area, and with it the most valuable distinction in the whole unit — the difference between the edge and the surface. Skipping the perimeter year and going straight to area formulas is the usual cause of students who can calculate both and confuse them.
Frequently asked questions
What is the difference between area and perimeter, for a student?
Perimeter is how far it is to walk all the way around the edge. Area is how much surface is inside. The fence and the paint is the version most students keep.
Are these worksheets in inches or centimeters?
Inches, feet and yards throughout, with areas in square inches and square feet.
What grade is perimeter taught?
Grade 3 in most US districts, with area following in Grade 4 or 5 depending on the sequence.
Do they cover 3D shapes?
Only in passing, in the Grade 2 sheet, where students sort flat shapes from solid ones. Volume and nets are not in this first set.
More free printable worksheets
Every set on this site is a free PDF, no sign-up needed. These are the other collections:
- Pre-Writing and Tracing Worksheets for Preschool
- Number Tracing Worksheets, 1 to 20
- Fractions Worksheets for Grades 3-6
- Multiplication Facts Worksheets and Times Tables
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