Third Grade Math Concepts: What Is a Perfect Square?

What Is a Perfect Square?

Qualities of Squares

Squares belong to the geometric class called quadrilaterals. A quadrilateral is a shape with four sides and can include a rhombus (or diamond), a rectangle or a perfect square. A perfect square is called a 'regular quadrilateral.' A rectangle is a square in which two sides are one length and the other two sides are another length. Only a perfect square has four equal sides and four equal angles. The angles will all be 90-degree (also called 'right') angles.

Practice Folding

You can create perfect squares out of printer or notebook paper. Take a sheet of paper and lay it down so that the tall side is vertical (up and down, rather than side to side). The sheet of paper is currently a rectangle. Fold the upper right-hand corner of the page over until the corner lines up with the left side of the sheet. You should have some paper left over at the bottom, outside of the fold. Cut this bottom section off with a pair of scissors. Now you have a perfect square!

Inexpensive white paper napkins often come as perfect squares. If you take a square and fold it like we did in the above example, and you find that there's no part leftover at the bottom of the page, then you know that the shape is a perfect square.

Area of a Perfect Square

When calculating the area of a square, you can use the formula A = l x w. Remember, whenever the shape is a perfect square, its length and width will be exactly the same. As a result, you will be multiplying the same number. Here's a sample problem:

A perfect square measures five feet long. What is its area?

Because we're told that the shape is a perfect square, can figure out that the width of the square is also five feet. The area is 25 square feet because 5 x 5 = 25.

Finding a Square's Perimeter

You can also find the perimeter of perfect squares by adding up the length of its sides. Because a perfect square's sides are all the same length, perimeter is easy to calculate. Using the example from above, the perimeter can be found by adding: P = 5 + 5 + 5 + 5 = 20 feet. Because the square has four sides, you can also multiply, like this: 4 x 5 = 20 feet.