The Most Common Shapes and How to Identify Them

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What Is a Shape?

If someone asks you what a shape is, you’ll likely be able to name quite a few of them. But “shape” has a specific meaning, too—it’s not just a name for circles, squares, and triangles.

A shape is the form of an object—not how much room it takes up or where it is physically, but the actual form it takes. A circle isn’t defined by how much room it takes up or where you see it, but rather the actual round form that it takes.

A shape can be any size and appear anywhere; they’re not constrained by anything because they don’t actually take up any room. It’s kind of hard to wrap your mind around, but don’t think of them as being physical objects—a shape can be three-dimensional and take up physical room, such as a pyramid-shaped bookend or a cylinder can of oatmeal, or it can be two-dimensional and take up no physical room, such as a triangle drawn on a piece of paper.

The fact that it has a form is what differentiates a shape from a point or a line.

The 6 Main Types of Two-Dimensional Geometric Shapes

Picturing a shape just based on definition is difficult—what does it mean to have form but not take up space? Let’s take a look at some different shapes to better understand what exactly it means to be a shape!

We often classify shapes by how many sides they have. A “side” is a line segment (part of a line) that makes up part of a shape. But a shape can have an ambiguous number of sides, too.

Type 1: Ellipses

Ellipses are round, oval shapes in which a given point (p) has the same sum of distance from two different foci.

Oval

An oval looks a bit like a smooshed circle—rather than being perfectly round, it’s elongated in some way. However, the classification is imprecise. There are many, many kinds of ovals, but the general meaning is that they are a round shape that is elongated rather than perfectly round, as a circle is. An oval is any ellipses where the the foci are in two different positions.

Because an oval is not perfectly round, the formulas we use to understand them have to be adjusted.

It’s also important to note that calculating the circumference of an oval is quite difficult, so there’s no circumference equation below. Instead, use an online calculator or a calculator with a built-in circumference function, because even the best circumference equations you can do by hand are approximations.

Definitions

Major Radius: the distance from the oval’s origin to the furthest edge
Minor Radius: the distance from the oval’s origin to the nearest edge

Circle

How many sides does a circle have? Good question! There’s no good answer, unfortunately, because “sides” have more to do with polygons—a two-dimensional shape with at least three straight sides and typically at least five angles. Most familiar shapes are polygons, but circles have no straight sides and definitely lack five angles, so they are not polygons.

So how many sides does a circle have? Zero? One? It’s irrelevant, actually—the question simply doesn’t apply to circles.

A circle isn’t a polygon, but what is it? A circle is a two-dimensional shape (it has no thickness and no depth) made up of a curve that is always the same distance from a point in the center. An oval has two foci at different positions, whereas a circle's foci are always in the same position.

Definitions

Origin: the center point of the circle
Radius: the distance from the origin to any point on the circle
Circumference: the distance around the circle
Diameter: the length from one edge of the circle to the other
π: (pronounced like pie) 3.141592…; thecircumferenceofacircletheradiusofacircle; used to calculate all kinds of things related to circles

Type 2: Triangles

Triangles are the simplest polygons. They have three sides and three angles, but they can look different from one another. You might have heard of right triangles or isosceles triangles—those are different types of triangles, but all will have three sides and three angles.

Because there are many kinds of triangles, there are lots of important triangle formulas, many of them more complex than others. The basics are included below, but even the basics rely on knowing the length of the triangle’s sides. If you don’t know the triangle’s sides, you can still calculate different aspects of it using angles or only some of the sides.

Definitions

Vertex: the point where two sides of a triangle meet
Base: any of the triangle’s sides, typically the one drawn at the bottom
Height: the vertical distance from a base to a vertex it is not connected to

Type 3: Parallelograms

A parallelogram is a shape with equal opposite angles, parallel opposite sides, and parallel sides of equal length. You might notice that this definition applies to squares and rectangles—that’s because squares and rectangles are also parallelograms! If you can calculate the area of a square, you can do it with any parallelogram.

Definitions

Length: the measure of the bottom or top side of a parallelogram
Width: the measure of the left or right side of a parallelogram

Rectangle

A rectangle is a shape with parallel opposite sides, combined with all 90 degree angles. As a type of parallelogram, it has opposite parallel sides. In a rectangle, one set of parallel sides is longer than the other, making it look like an elongated square.

Because a rectangle is a parallelogram, you can use the exact same formulas to calculate their area and perimeters.

Square

A square is a lot like a rectangle, with one notable exception: all its sides are equal length. Like rectangles, squares have all 90 degree angles and parallel opposite sides. That’s because a square is actually a type of rectangle, which is a type of parallelogram!

For that reason, you can use the same formulas to calculate the area or perimeter of a square as you would for any other parallelogram.

Rhombus

A rhombus is—you guessed it—a type of parallelogram. The difference between a rhombus and a rectangle or square is that its interior angles are only the same as their diagonal opposites.

Because of this, a rhombus looks a bit like a square or rectangle skewed a bit to the side. Though perimeter is calculated the same way, this affects the way that you calculate the area, because the height is no longer the same as it would be in a square or rectangle.

Definition

Diagonal: the length between two opposite vertices

Type 4: Trapezoids

Trapezoids are four-sided figures with two opposite parallel sides. Unlike a parallelogram, a trapezoid has just two opposite parallel sides rather than four, which impacts the way you calculate the area and perimeter.

Definitions

Base: either of a trapezoid’s parallel sides
Legs: either of the trapezoids non-parallel sides
Altitude: the distance from one base to the other

Type 5: Pentagons

A pentagon is a five-sided shape. We typically see regular pentagons, where all sides and angles are equal, but irregular pentagons also exist. An irregular pentagon has unequal side and unequal angles, and can be convex—with no angles pointing inward—or concave—with an internal angle greater than 180 degrees.

Because the shape is more complex, it needs to be divided into smaller shapes to calculate its area.

Definitions

Apothem: a line drawn from the pentagon’s center to one of the sides, hitting the side at a right angle.

Type 6: Hexagons

A hexagon is a six-sided shape that is very similar to pentagon. We most often see regular hexagons, but they, like pentagons, can also be irregular and convex or concave.