# Apex|Definition & Meaning

## Definition

An **apex, **in geometry, is the **vertex** that is at the most **heightened** point of a certain shape. The term is **generally** used to direct to the vertex **opposite** to the base. The phrase **Apex** is taken from the Latin for peak, **summit, tip, extreme** end, and **top.**

An **apex** is the most heightened **juncture** of certain shapes. Mount **Everest’s** apex is the **peak** of the **mountain.** The apex is **usually** found at a **vertex.** A **vertex** is a single **point** where two or more lines, **curves,** or sides meet. The **apex** is found right at the **highest** point over or **opposite** the underside of the **body** called a **base**.

The **highest** point on the earth is Mount **Everest,** at the **evaluation** of **29,000 feet**. People who reach the top of **mount Everest,** reach the most **heightened** point on the earth. The **apex** of the earth is the peak of **Mount Everest.**

**Apex in Isosceles Triangles**

An **apex** is the most **elevated** point of a **certain** 2D and 3D figure relative to the base of a **figure.** Additionally, the **phrase** apex is usually used to **direct** to the most **heightened** vertex opposite to the base of a **geometric** figure. Below are some **illustrations** of geometric figures and their **respective** apex:

Apex in an **isosceles** triangle shown in **figure 1** is the **vertex** where the two sides of the **same** size meet, **opposite** the base that is the **unequal third side.** The **isosceles** triangle’s vertex **having** an angle **distinct** from the two **identical** angles is called the **isosceles triangle’s apex.**

A **triangle** that has a **minimum** of two sides of **equal** length is called an **isosceles** triangle. Sometimes it is **defined** as having strictly two sides of **equal** length, and sometimes as having a **minimum** of two sides of the same **length.** The two equal sides are named the **legs** and the third side is **named** the **triangle’s** base. The other parameters of the **triangle,** like its area, height, and **perimeter** can be estimated by easy formulas from the **measurements** of the legs and base. The two angles **opposite** the legs are **similar** and **acute.**

**Apex in Cone**

The **apex** in a cone or **pyramid** is the vertex at the top which is **opposite** the base. The **geometric** shape of a cone is **three-dimensional** and it **tapers** smoothly from a **balanced** base to a point known as the **apex.**

A **cone** is constructed by a set of **line** segments. The **lines** join a shared **point,** the apex which is **opposite** to the base. The **base** may be **limited** to a **circle,** a **quadratic** form of any **one-dimensional** in the plane, or any **one-dimensional** closed figure, If the **enclosed** points are incorporated in the base, the **cone** is a solid entity, **otherwise,** it is a **two-dimensional** entity in a **three-dimensional** span. In the case of a **solid** object, the border formed by these lines is anointed as the lateral surface and it is said to be a conical surface if the lateral surface is **unbounded.**

In line **segments,** the cone does not spread **beyond** the base whereas in the case of lines, the cone spreads **infinitely** away in both directives from the **apex,** in which case it is occasionally named a **double** cone.

**Apex in Pyramid**

The **apex** of a right **pyramid** is directly **above** the centroid of its base. The **base** of a regular **pyramid** is like of a regular **polygon** and is usually **insinuated** to be a right **pyramid.**

**A pyramid** in geometry **is** a polyhedron composed by **joining** a polygonal base and a point, named the **apex.** Per apex and **base** edge form a **triangle** named a lateral face. It is a **conic** entity with a **polygonal** base. an **n-sided** base of a pyramid has **n + 1 vertice**s,** 2n edges**, and **n + 1 faces**.

When unidentified, a pyramid is **commonly** assumed to be a standard square pyramid, like the physical pyramid designs. A **tetrahedron** is a name often given to the **triangle-based** pyramid. A **pyramid** is named acute if its apex is over the interior of the base and if its apex is over the exterior of the base then it’s **called** obtuse. The apex of **the right-angled pyramid** is over a vertex or edge of the **base.**

**Height in Apex**

The figure’s apex is usually **associated** with the height of the **figure.** The peak of a figure can be typically **defined** as the **perpendicular** length from the base of the **figure** to the flank opposite the base. If the **figure** has the **apex,** the peak of the figure is the **perpendicular** length from the **apex** to the base of the **figure.**

Hence, when a **figure** has an **apex,** the extreme **peak** of the figure **contains** the apex of the **figure,** but the **apex** just defines the **highest juncture,** while the peak is a **measurement** of **distance.**

**Solving Apex: An Example**

Does the **apex** exist in the **prism** shown below?

### Solution

No, the **apex** of such geometric **figures** does not exist. The **explanation** is, the phrase apex is **only** used to define **particular** geometric figures. The above geometric figure has **multiple** points to be viewed at an apex. Thus, the phrase apex is only and **truly** used in geometric **figures** like triangles, cones, **pyramids,** and other **figures** in which there is solely one **most** heightened vertex opposite the figure’s base. **Otherwise,** it would not be **obvious** what point is being directed to as the **apex.**

In the **rectangular** prism shown above, we **could** technically direct to four **different** points opposite to a base as an **apex.** The red points in the figure symbolize four **apices** of the cube. Also, each of the four **points** in the figure has the **exact** same height as any juncture on the **face** of the prism **opposite** the **desired** base, so none of the **apices** would hold the **description** of being the **most elevated** point, since **they** would all be the **most** elevated point of the **prism.**

*All images/graphs are created using GeoGebra.*