What is a Square?
A quadrilateral with four equal sides and four equal (right) angles
A square is a flat shape (polygon) that has four equal sides and four equal angles. Each angle in a square is a right angle (90°).
Let’s recap the properties of a square:
- All four sides are equal in length.
- All four angles are right angles (90°).
- Opposite sides are parallel.
- It has 2 lines of symmetry across the diagonals and 2 lines of symmetry across the middle (vertical and horizontal).
- The diagonals are equal in length and intersect at right angles.
We can also describe a square as:
- A special type of rectangle and rhombus because it shares their properties: right angles (like rectangles) and equal sides (like rhombi).
- A two-dimensional figure; its dimensions are height and width, which are equal in size. Its three-dimensional counterpart is a cube, which has a third dimension: depth.
Since squares are two-dimensional, flat shapes, we usually encounter them in drawings, on screens, or as faces of a cube or another three-dimensional shape. We can see squares on:
- Pizza boxes
- A chessboard square
- Floor tiles
- Dice
- Cheese slices
- Crackers
Area and Perimeter of a Square:
- Area = side × side (s²)
- Perimeter = 4 × side (4s)
When Do Students Learn About Squares?
Students are introduced to squares early in their study of shapes and build on this knowledge as they learn more about geometry.
Grades 1–2 – Recognizing Squares
Students identify squares among other shapes and learn about equal sides and right angles.
Grades 3–5 – Working with Squares
Students learn to calculate perimeter and area of squares and explore their properties within geometry.
Grades 6+ – Squares in Geometry and Algebra
Students use squares in more advanced geometry, study square roots, and explore squares in algebraic contexts (e.g., x²).
