Contents

# Flat|Definition & Meaning

## Definition

In **mathematics,** the term flat refers to a surface that is **uniform, smooth,** or plane. A flat surface represents a horizontal plane and does not have any **depth**. Examples include planar and **two-dimensional** shapes, etc.

A **significant** portion of geometry is concerned with **two-dimensional** figures, like **squares,** circles, and **triangles,** which can be drawn on a sheet of paper. The study of **spheres,** cones, and cubes, along with other **three-dimensional** solid objects that are all around us, is what solid geometry is all about.

The part of an object that is **visible** to us and is located on its exterior is **referred** to as the surface of the thing. It does not have any **thickness,** but it does have an area. **Smoothness** can be seen, for instance, on the surface of a mirror. The surfaces of these solids might be flat or **curved, depending** on their shape.

A few good examples of flat **surfaces** include the **surface** of the walls, the floor, the tabletop of a table, and paper. In addition, the exterior of **spheres, eggs,** and **even lemons** have a curved **shape.** Examine the **figure below** for several illustrations of surfaces that are **both** flat. In the figure below, the **square** has 4 **flat surfaces** while the **other figure** has **0** flat **surface,** which is a **circle.**

## What Are Flat Shapes in Math?

In **mathematics,** there are two different **kinds** of **shapes: two-dimensional** and three-dimensional. The **two-dimensional** flat **shapes** are solely **two-dimensional,** that is, they have **length** and width but no thickness. Any flat **surface** or piece of paper can be used to draw **flat forms.**

Some examples of flat shapes in **mathematics include** the **square, rectangle, circle,** diamond, and triangle.

**Square**

A **square** is a shape that only **exists** in two **dimensions** and is flat. It has four sides that are all the same **length** and four **vertices.** The level land area that is **completely** contained within a **square** is **referred** to as a square region.

**Example**

A **good** illustration of a **square** is a wall or **table** that is **completely square** and has four **sides** that are all the **same** length.

** **

**Rectangle**

A **rectangle** is a form that is flat and only has **two dimensions.** Its opposite sides generally equal in **length** and parallel to one another. The term **“rectangular** region” **refers** to the level of land that lies inside the **boundaries** of the **rectangle.**

** ****Example**

**Some examples** of **objects** that have a **rectangle** shape include the **chalkboard,** notes for the rupee and the **dollar,** and so on.

**Triangle**

A **triangle** is a type of **polygonal** flat shape **which** has three **vertices** and three sides, **making** it a three-sided polygon. The term **“triangular** region” refers to the level **area** that is **contained** inside the **confines** of the **triangle.**

**Example**

**One** of the most well-known and impressive **examples** of a **triangular** shape is a **pyramid.**

**Circle**

The **circle** is indeed a shape that only exists in **two dimensions** and has a flat **perimeter** that is curved. The **circle** lacks both sides and corners all the way **around.** The region that can be found inside a **circle** is referred to as the **circular** region.

**Example**

A few **examples** of objects that have **circular** shapes **include** the **disc,** pizza, and **wall clock.**

**Octagon**

The **octagon** is a flat, flat **shape** with **eight** sides. It is a shape with eight sides. The area inside the octagon that is flat is called the **octagonal** region.

**Example**

The **roadside** stop **sign** is a great example of an octagon shape.

**Definitions of Common Solid and Three-Dimensional Shapes**

A **shape** that **occupies** space is referred to as a solid or a three-dimensional shape. They have three **dimensions:** the **length,** the width, and the height of the object. They are everything within our grasp at this **moment.** They are present in the activities that we do on a **regular** basis. Solid shapes include things like your **books** and a **football,** for **instance.**

There are several **characteristics** that are consistent **throughout** all the 3D shapes. Faces, edges, as well as vertices or corners, are all examples of these types of characteristics.

The flat **surface** of such a solid is also known as the face of a solid. A **solid’s** face can be any flat shape, including squares, **circles,** triangles, etc. The edge is indeed the line **segment** that connects two **faces** of a solid. The **place** where two or even more edges meet is known as the vertex.

A solid shape may have a single surface or several surfaces. Let’s **investigate** the various surface kinds that solid shapes can have.

## In Geometry, What Is a “Flat Surface”?

In the field of **geometry,** a plane is another name for a **level** surface. Plane geometry **focuses** on shapes that are **flat** and **two-dimensional,** like **squares,** circles, and **triangles,** which can be **drawn** on a **piece** of **paper.** Length and width are the two **dimensions** that make up a **plane** or **flat shape.**

A shape that **occupies** space is **referred** to as a **solid** or a **three-dimensional** shape. The term **“surface”** refers to the layer of such **solid** that is located at its outside. It is referred to as a flat **surface** whenever the **surface** of the solid is indeed a plane surface without any depths, which is another way of **saying** that it is flat.

Every day, we **encounter** a variety of flat objects in our **environment.** For example, the top of a **book,** a **table,** or a dresser can have a flat **surface.**

**How to Recognize Flat Surfaces in 3D Forms**

According to the **previous** section, a solid’s **surface** can be **flat** or curved. The surface of a three-dimensional shape is a planar figure, including such squares, circles, and triangles.

**Observing** cubes, cuboids, **pyramids,** and prisms in three **dimensions** reveals that they have only flat or **level** surfaces. **Three-dimensional** figures and shapes, such as a cylinder or cones, consist both of flat as well as curved surfaces. In addition, particular **three-dimensional** structures, such as **spheres,** have no flat surfaces and only one curved surface.

An object with a flat surface can be slid. If such an **object** seems to have a **curved** surface, it is **possible** to roll it along **that** surface.

## An Example of Flat Shapes and Surfaces

### Example

In the **following** figure below, how many flat **surfaces** are there?

### Solution

The **given** figure is of the cone.

As we **can** see:

The **number** of **flat surfaces** = 2

The **number** of **curved surfaces** = 1

*All mathematical drawings and images were created with GeoGebra.*